CBSE Class 9 Mathematics Surface areas and Volumes Assignment Set B

Question. The cardboard piece shown below can be folded up along the dotted lines to form a triangular pyramid.Which of the following is a view of the pyramid formed?

Answer : A

Question. The container shown here is filled with water from a uniformly dripping tap.Which of these graphs best represents the water level in the container with respect to time, as it is being filled?

Answer : A

Question. One man takes one day to dig a 4 m long trench. How long would it take 2 men working at the same rate to dig a 16 m long trench?
A. 1 day
B. 2 days
C. 4 days
D. 8 days
Answer : B

Question. A cake is cut into 3 pieces whose weights are in the ratio 2 : 1 : 4.If the third piece weighs 360 g more than the second, how much did the whole cake weigh?

A. 1.44 kg
B. 1.26 kg
C. 840 g
D. 630 g
Answer : C

Question. A solid shape made by joining identical cubes is placed on a table. When viewed from different sides, the solid looks as shown below.Which of these could be the solid?

Answer : D

Question. Sonali has about half a litre of molten wax to make a candle. Which of these candles could she have made using the ENTIRE quantity of wax?

Answer : B

Question. Zubin wants to cover the CURVED SURFACE of an old waste paper basket with colored paper. The dimensions of the basket are shown below. What is the total area that has to be covered with paper? 

A. 220 cm²
B. 440 cm²
C. 880 cm²
D. 1760 cm²
Answer : C

Question. An ant at one corner of an 8 m x 6 m rectangular floor spots a piece of sweet at the opposite corner.What is the MINIMUM distance the ant has to travel to reach the sweet?

A. 7 m
B. 10 m
C. 14 m
D. 28 m
Answer : B

Question. Aftab is checking his weight on a weighing scale. What is the reading on the scale, shown in the Image?

A. 50.3 kg
B. 50.7 kg
C. 52 kg
D. 53.5 kg
Answer : D

Question. Travelling only along the edges and covering a distance of exactly 22 cm, how many different routes can be taken to go from corner P to corner Q of this cuboid?

A. 10
B. 8
C. 6
D. 1
Answer : D

Question. Which of these could be the approximate width of a regular sized basketball court?
A. 5 m
B. 15 m
C. 35 m
D. 50 m
Answer : B

Question. Dalbir has to carve a right circular cylinder of the maximum possible volume from this wooden cuboid shown in the image .What would be the volume (in cm3) of the cylinder?

A. 3000 π
B. 4000 π
C. 4500 π
D. 16000 π
Answer : B

Question. 4 identical triangles are cut off from the 4 corners of a square of side 20 cm as shown in the image.By how much did the perimeter decrease (with respect to the original square)?

A. 4 cm
B. 8 cm
C. 24 cm
D. 28 cm
Answer : B

Question. When an A-4 sized sheet of paper is folded up once through the centre as shown, the 'length to breadth'  ratio of the folded up piece is the same as the 'length to breadth' ratio of the original sheet.What is the 'length to breadth' ratio of an A-4 sized sheet? 

A. √2 : 1
B. 03:02 
C. 02:01
D. (information insufficient) 
Answer : A

Question.  The diamet er of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas.
(A) 2:3
(B) 4:5
(C) 5:4
(D) 3 :2
Answer : A

Question. The circumference of the base of a 9 m high wooden solid cone is 44 m. Find the slant height of the cone.
(A) √120
(B) √l30m
(C) √150m
(D) 7√5m
Answer : B

Question. A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. (Take π = 22/7)
(A) 8 cm
(B) 9 cm
(C) 10 cm
(D) 11 cm
Answer : B

Question. Find the volume of a cube whose surface area is 150 cm².
(A) 25J5 cm³
(B) 64 cm³
(C) 125 cm³
(D) 27 cm³
Answer : C

Question. The circumference of the base of 9 m high wooden solid cone is 44 m. Find its volume. (Use π = 22/7)
(A) 235m³
(B) 456m³
(C) 365m³
(D) 462m³
Answer : D

Question. On a particular day, the rain fall recorded on a terrace 6 m long and 5 m broad is 15 cm. Find the quantity of water collected on the terrace.
(A) 300 litres
(B) 450 litres
(C) 3000 litres
(D) 4500 litres
Answer : D

Question. The height of sand in a cylindrical box drops 3 inches when 1 cubic foot of sand is poured out . What is t he diameter, in inches, of the cylinder?
(A) 24/√n
(B) 48/√n
(C) 32/√n
(D) 48/n
Answer : B

Question. The total surface area of a cylinder of height 6.5 em is 220 sq cm. Find its volume.
(A) 25.025 cm³
(B) 2.5025 cm³
(C) 2502.5 cm³
(D) 250.25 cm³
Answer : D

Question. The height of a cylinder is 15 cm. The curved surface area is 660 sq. m. Find its radius.
(Take π as 22/7)
(A) 7 cm
(B) 9 cm
(C) 6 cm
(D) 11 cm
Answer : A

Question. A cylindrical vessel contains 49.896 litres of liquid.Cost of painting its C.S.A.at 2 paise/sq em is ₹ 95.04. What is its total surface area?
(A) 5724 cm²
(B) 7524 cm²
(C) 5742 cm²
(D) 7254 cm²
Answer : B

Case Based MCQs

Case I : Read the following passage and answer the questions from 1 to 5.
Nakul was doing an experiment to find the radius r of a ball. For this he took a cylindrical container with radius R = 7 cm and height 10 cm. He filled the container almost half by water as shown in the figure-1. Now he dropped the ball into the container as in figure-2.
He observed that in figure-2, the water level in the container raised from P to Q i.e, to 3.4 cm.

1. What is the approximate radius of the ball?
(a) 3 cm
(b) 5 cm
(c) 7 cm
(d) 9 cm
Answer : B

2. What is the volume of the cylinder?
(a) 1260 cm²
(b) 540 cm³
(c) 1620 cm³
(d) 1540 cm³
Answer : D

3. What is the volume of the spherical ball?
(a) 620 cm³
(b) 824.26 cm³
(c) 523.81 cm³
(d) 430.1 cm³
Answer : C

4. How many litres of water can be filled in the full container ?
(a) 1.54 litres
(b) 2 litres
(c) 5 litres
(d) 7.5 litres
Answer : B

5. What is the total surface area of the spherical ball?
(a) 441.34 cm²
(b) 314.29 cm²
(c) 620 cm²
(d) 816 cm²
Answer : A

Very Short Answer Type Questions

Question. The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. Find the radius of the sphere.
Answer : 6 cm

Question. Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9cm.
Answer : 190.93cm³

Question. A toy is in the form of a cone mounted on a hemi-sphere of same radius. The diameter of the base of the conical part is 7cm and the total height of the toy is 14.5cm. find the volume of the toy.
Answer : 231cm³

Question. The TSA of a solid cylinder is 231cm². If its CSA is 2/3 of its TSA. Find its radius and height.
Answer : 3.5cm, 7cm

Question. How many bags of grain can be stored in a cubic granary 12m x 6m x 5m , if each bag occupies a space of 0.48 m³ ?
Answer : 750

Question. The volume of two cubes are in the ratio 8 : 64 , then find the ratio of their surface areas.
Answer : 4 : 9

Question. A cone and a hemisphere have equal bases and equal volumes. What is the ratio of their heights?
Answer : 2 : 1

Question. The radii of 2 cylinders are in the ratio 3:5 and their heights are in the ratio 2:3. What is the ratio of their curved surface areas.
Answer : 2:5

Question. A cylinder and a cone are of same base radius and of same height. What is the ratio of their volumes?
Answer : 3 : 1

Question. Find the Total Surface Area of a hemispherical solid having radius 7 cm.
Answer : 462

Question. Two cubes each of volume 27cm³ are joined end to end to form a solid. Find the surface area of the solid.
Answer : 90cm²

Question. The length of a hall is 20m and width is 16m. the sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.
Answer : 8.8m

Question. A cone and a cylinder of same radius 3.5cm have same CSA. If height of the cylinder is 14cm then find the slant height of the cone.
Answer : 28cm

Short Answer Type Questions

Question. The radius of the circular part of a hemispherical bowl is 9 cm. Find the total capacity of 21 such bowls.
Answer : Volume of one bowl = Volume of hemisphere
= (2/3)πr³ = (2/3 x 22/7 x 9³) cm³
Capacity of 21 such bowls = 21 × 2/3 x 22/7 × 9³ = 32076 cm³

Question. The dome of a building is in the form of a hemisphere. If its radius is 14 cm, find the cost of painting it at the rate of ₹ 3 per sq. cm.
Answer : Since the dome of building is in the shape of hemisphere
⇒ Curved surface area of dome = 2πr²
= 2 × 22/7 × 14 × 14 = 2 × 22 × 2 × 14 = 1232 cm²
Cost of painting the dome at the rate of 1 sq. cm = ₹ 3
∴ Cost of painting of 1232 cm² dome
= ₹ 3 × 1232 = ₹ 3696

Question. A cube of 8 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of its base are 17 cm and 14 cm. Find the rise in water level in the vessel
Answer : Edge of the cube = 8 cm
∴ Volume of the cube = a³ = (8)³ = 512 cm³
If the cube is immersed in the vessel, then the water level rises. Let the rise in water level be x.
Clearly, Volume of the displaced water = Volume of the cube
⇒ Volume of the cube = 17 cm × 14 cm × x cm
⇒ 512 = 17 × 14 × x
⇒ x = 512/17x14 ⇒ x = 512/238 = 2.15 cm

Question. The length of a cold storage is three times its breadth. Its height is 5 m. The area of its four walls (including doors) is 256 m². Find its volume.
Answer : Let length, breadth and height of the cold storage be l, b and h respectively.
Then, l = 3b and h = 5 m.
Now, area of four walls = 256 m²
⇒ 2 (l + b)h = 256 ⇒ 2 (3b + b) × 5 = 256
⇒ 40b = 256 ⇒ b = 6.4 metres
∴ l = 3b = 3 × 6.4 = 19.2 m
Volume of the cold storage = l × b × h
= (19.2 × 6.4 × 5) m3 = 614.4 m³

Question. The curved surface area of a cone is 154 cm². If its radius is x cm and slant height is 7 cm. Find the value of 20x.
Answer : We have, curved surface area = 154 cm²
⇒ πrl = 154 ⇒ r = 154x7/22x7 = 7
Now, r = x cm = 7 cm.
∴ x = 7 ⇒ 20x = 20 × 7 = 140

Question. If the height of a cylinder is 11 cm and area of curved surface is 968 sq. cm. Find the radius of the cylinder.
Answer : Height of cylinder = 11 cm
Curved surface area = 968 cm²
⇒ 2πrh = 968
⇒ 2x22/7 × π × 11 = 968 ⇒ r = 14 cm

Question. The base of a cubical box has a perimeter 250 m. Find the cost of painting its lateral surface area at the rate of ₹ 10 per m².
Answer : Let the side of cubical box be a m.
Perimeter of base of a cubical box = 4a m
⇒ 250 = 4a ⇒ a = 62.5 m
Now, LSA of cubical box = 4a² = 4 × (62.5)² = 15625 m²
Cost of painting 1 m² = ₹ 10
∴ Total cost of painting = 15625 × 10 = ₹ 156250.

Question. A cuboidal oil tin box is 4 m by 2 m by 0.75 m. Find the cost of the tin sheet required for making 20 such tin boxes, if the cost of tin sheet is ₹ 20 per square metre.
Answer : Length, l = 4 m, breadth, b = 2 m and
height, h = 0.75 m
Surface area of one tin box = 2(lb + bh + hl)
= 2 (4 × 2 + 2 × 0.75 + 0.75 × 4)
= 2 (8 + 1.5 + 3) = 2 × 12.5 = 25 m²
∴ Surface area of 20 such tin boxes = (20 × 25) m²
= 500 m²
Now, cost of 1 square metre of tin sheet = ₹ 20
∴ Cost of 500 m² of tin sheet = ₹(20 × 500) = ₹ 10000

Question. Three cubes each of edge 5 cm are joined end to end. Find the surface area of the resulting cuboid
Answer : When three cubes are joined end to end, we get a cuboid such that
Length of the resulting cuboid, l
= 5 cm + 5 cm + 5 cm = 15 cm
Breadth of resulting cuboid, b = 5 cm
Height of the resulting cuboid, h = 5 cm
Surface area of the cuboid = 2 (lb + bh + hl)
= 2 (15 × 5 + 5 × 5 + 5 × 15) cm²
= 2 (75 + 25 + 75) cm² = 350 cm²

Question. Find the diameter of the sphere, whose total surface area is 616 cm²
Answer : Let r be the radius of the sphere.
Total surface area of sphere = 4πr²
⇒ 616 = 4 × 22/7 ×r² ⇒ = r² 616x7/4x22 = 49 ⇒ r = 7 cm
∴ Diameter = 2r = 2 × 7 = 14 cm

Question. Find the volume of a lead pipe 3.5 m long, if the external diameter of the pipe is 2.4 cm, thickness of lead is 3 mm and 1 cm³ of lead weighs 12 g
Answer : External diameter of the pipe = 2.4 cm
External radius of the pipe, (R) = 2 4/2. cm =1.2 cm
Thickness of the pipe = 3 mm = 0.3 cm
Internal radius, (r) = External radius – thickness
= 1.2 cm – 0.3 cm = 0.9 cm
Length of the pipe (h) = 3.5 m = 350 cm
Volume of lead = π(R² – r²)h
= 22/7× [(1.2)² – (0.9)²] × 350 = 22/7× 0.63 × 350 = 693 cm³

Question. Find the total surface area, lateral surface area and the length of diagonal of a cube, each of whose edges measues 20 cm.
(Take √3 = 1.732)
Answer : Here, side (a) = 20 cm
∴ Total surface area of the cube = 6a² = 6(20)²
= 2400 cm²
and, lateral surface area of the cube = 4a² = 4(20)²
= 1600 cm²
Also, length of diagonal of a cube = √3a
= √3 × 20= (1.732 × 20) = 34.64 cm.

Question. A room is 16 m long, 9 m wide and 3 m high. It has two doors, each of dimensions (2 m × 2.5 m)and three windows, each of dimensions (1.6 m × 75 cm). Find the cost of distempering the walls of the room from inside at the rate of ₹ 8 per sq. metre.
Answer : Given, length (l) = 16 m, breadth (b) = 9 m and
height (h) = 3 m
∴ Area of 4 walls of the room = 2(l + b) × h
= 2(16 + 9) × 3 = 150 m².
Area of 2 doors = 2 × (2 × 2.5) = 10 m²
Area of 3 windows = 3 × (16 × 75/100) = 3.6 m².
Area not to be distempered = 10 + 3.6 = 13.6 m²
Area to be distempered = 150 – 13.6 = 136.4 m²
Cost of distempering the walls = ₹ (136.4 × 8) = ₹ 1091.20

Question. The total cost of making a solid spherical ball is ₹ 67914 at the rate of ₹ 14 per cubic metre. Find the radius of this ball.
Answer : Volume of spherical ball = Total cost/Cost of 1m³
⇒ (4/3)πr³ = 67914/14 ⇒ 4/3 x 22/7 x r² = 67914/14
⇒ r³ = 101871/88  ⇒ r³ = 1157.625 ⇒ r = 10.5 m

Question. The external diameter of an iron pipe is 35 cm and its length is 30 cm. If the thickness of the pipe is 2.5 cm, find the curved surface area of the pipe.
Answer : Length of the pipe, h = 30 cm
External radius of the pipe, R = 35/2 cm = 17.5 cm
∴ Thickness of the pipe = 2.5 cm
∴ Internal radius of the pipe, r = (17.5 – 2.5) cm = 15 cm
Now, curved surface area of the pipe = External curved surface area + Internal curved surface area
= 2πRh + 2prh = 2πh (R + r)
= 2 × 22/7 × 30(17.5 + 15) = 2 × 22/7 × 30 × 32.5
= 42900/7 = 6128.57 cm²

Question. A closed cuboidal tank can store 5040 litres of water. The external dimensions of the tank are 2.2 m × 1.7 m × 1.7 m. If the walls of the tank are 5 cm thick, then what is the thickness of the bottom (top) of the tank if they are same?
Answer : Capacity of tank = 5040 litres
= (5040'1000)m³ = 5.040m³
Internal length of tank = (2 2 - 2 x 5/100) m = 2.1m
Internal breadth of tank = (1 7 - 2 x 5/100) m = 1.16 m
Let the thickness of tank in the bottom be x m.
Internal height of tank = (1.7 – 2x) m
Now, Internal volume of tank = Capacity of tank
⇒ 2.1 × 1.6 × (1.7 – 2x) = 5.040
⇒ 1.7 - 2x = 5.040/2.1 x 1.6 = 1.5
⇒ 2x = 1.7 – 1.5 = 0.2
⇒ x = 0.1 m = 0.1 × 100 cm = 10 cm
So, required thickness = 10 cm

Question. The slant height of a cone is 25 cm and  the vertical height is 24 cm. Find the radius and the total surface area of the cone.
Answer : Here, h = 24 cm and slant height (l) = 25 cm
Let r be the radius of cone. Then,
l² = h² + r²
⇒ r² = 252 – 242 = 49 ⇒ r = 7
Total surface area of the cone = πr(l + r)
= [22/7 x 7 x (25+7)] cm² = 704 cm²

Question. The length and breadth of a rectangular solid are respectively 35 cm and 20 cm. If its volume is 7000 cm³, then find its height (in cm).
Answer : Let h be the height of the solid.
∴ Volume of cuboid = l × b × h
⇒ 7000 = 35 × 20 × h ⇒ h = 7000 = 700/10 cm

Question. If volume and surface area of a sphere is numerically equal then find its radius (in units).
Answer : Let r be the radius of the sphere.
∴ Volume of sphere = Surface area of sphere
∴ (4/3)πr³ = 4πr² ⇒ r³/r² = 3 ⇒ r = 3 units

Question. Coins of same size (say 10 rupee coin) are placed one above the other and a cylindrical block is obtained. The volume of this block is 67.76 cm³. Find the number of coins arranged in the block, if thickness of each coin is 2 mm and radius of each coin is 1.4 cm.
Answer : Let h be the height of cylindrical block and n be the
number of coins used to obtain it.
Volume of block = πr2h ⇒ 67.76 = 22/7 × 1.4 × 1.4 × h
⇒ h = 67.76x7/22x1.4x1.4 = 11cm = 110mm       [∴ 1 cm = 10 mm]
Now, n × thickness of a coin = height of block
⇒ n × 2 = 110 ⇒ n = 5

 

Surface Areas and Volumes

Q 1 Find the area enclosed between two concentric circles of radii 4 cm and 3 cm.

Q 2 The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions?

Q 3 A cuboid has total surface area of 40 sq m and its lateral surface area is 26 sq m. Find the area of base.

Q 4 Three metal cubes whose edges measure 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the edge of the new cube. Also find the surface area of the new cube.

Q 5 An iron pipe 20 cm long has exterior diameter equal to 50 cm. If the thickness of the pipe is 1cm, find the whole surface area of the pipe.

Q 6 The lateral surface of a cylinder is equal to the curved surface of a cone. If the radius is the same, find the ratio of the height of the cylinder and slant height of the cone.

Q 7 A right circular cylinder just enclosed a sphere of radius r as shown in figure find the surface area of the sphere , curved surface area of the cylinder and also their ratio.

Q 8 A godown is in the form of a cuboid measuring 60 m x 40 m x 20 m. How many cuboidal boxes can be stored in it if the volume of one box 0.8 m³?

 

Click on link below to download CBSE Class 9 Mathematics Surface areas and Volumes Assignment Set B