CBSE Class 9 Mathematics Surface Areas And Volume VBQs

Question. If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?
(A) 4
(B) 1/2
(C) 2
(D) 1/2
Answer : B

Question. A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, then the amount of the beverage that can be poured from the bowl into the cylindrical vessel is ______.
(A) 66(2/3)%
(B) 78(1/2)%
(C) 100%
(D) None of these
Answer : C

Question. The edge of a cube is 20 cm. How many small cubes of edge 5 cm can be formed from this cube?
(A) 4
(B) 32
(C) 64
(D) 100
Answer : C

Question. The length of the longest rod that can be kept in a cuboidal room of dimensions 10 m × 10 m × 5 m is _____.
(A) 16 m
(B) 10 m
(C) 15 m
(D) 12 m
Answer : C

Question. A covered wooden box has the inner measures as 115 cm, 75 cm, 35 cm and the thickness of wood is 2.5 cm. Then the volume of the wood is ______.
(A) 80000 cu. cm
(B) 82125 cu. cm
(C) 84000 cu. cm
(D) 85000 cu. cm
Answer : B

Question. If the length of diagonal of a cube is √12cm, then the volume of the cube is
(A) 8√12 cm³
(B) 8 cm³
(C) 16√2 cm³
(D) 16 cm³
Answer : B

Question. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. Find the difference between surface areas of two solids.
(A) 280 cm²
(B) 284 cm²
(C) 296 cm²
(D) 286 cm²
Answer : D

Question. The height of a cone is equal to its base diameter. Then slant height of the cone is
(A) √r²+h²
(B) r√5
(C) h√5
(D) rh√5
Answer : B

Question. The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is the value of r in terms of x?
(A) x2/2π
(B) x/2√π
(C) √2x/π
(D) x/√π
Answer : B

Question. A spherical ball of lead, 3 cm in radius is melted and recast into three spherical balls. The radius of two of these are 1.5 cm and 2 cm respectively. The radius of the third ball is ______.
(A) 2.66 cm
(B) 2.5 cm
(C) 3 cm
(D) 3.5 cm
Answer : B

Question. How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall 8 m × 6 m × 22.5 cm?
(A) 5600
(B) 6000
(C) 6400
(D) 7200
Answer : C

Question. The volume of two spheres are in the ratio 64 : 27. The difference of their surface areas, if the sum of their radii is 7 units, is _____.
(A) 28p sq. units
(B) 88 sq. units
(C) 88p sq. units
(D) 4p sq. units
Answer : A

Question. How many metres of cloth, 5 m wide, will be required to make a conical tent, the radius of whose base is 7 m and height is 24 m?
(A) 550 m
(B) 168 m
(C) 110 m
(D) 33.6 m
Answer : C

Question. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.
(A) 266.11 cm³
(B) 301.12 cm³
(C) 242.36 cm³
(D) 278.34 cm³
Answer : A

Question. A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m × 25 m × 15 m.
For how many days will the water of this tank last?
(A) 30 days
(B) 32 days
(C) 40 days
(D) 45 days
Answer : C

Question. Match the following.

(A) (P)→(2) ; (Q)→(3) ; (R)→(4) ; (S)→(1)
(B) (P)→(1) ; (Q)→(3) ; (R)→(2) ; (S)→(4)
(C) (P)→(3) ; (Q)→(1) ; (R)→(2) ; (S)→(4)
(D) (P)→(4) ; (Q)→(1) ; (R)→(3) ; (S)→(2)
Answer : C

Question. Water flows in a tank 150 m × 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep?
(A) 50 hours
(B) 150 hours
(C) 100 hours
(D) 200 hours
Answer : C

Question. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes is _____.
(A) 10 : 17
(B) 20 : 27
(C) 17 : 27
(D) 20 : 37
Answer : B

Question. A circus tent is cylindrical to a height of 3 metres and conical above it. if its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.
(A) 1996 m
(B) 2096 m
(C) 1947 m
(D) 1800 m
Answer : C

Question. A teak wood log is first cut in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is 1.104 m3. How many rectangular planks of size 2.3 m × 0.75 m × 0.04 m can be cut from the cuboid?
(A) 16
(B) 64
(C) 68
(D) 4
Answer : A

Question. A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, then how many litres of milk is needed to serve 1600 students?
(A) 739.2 litres
(B) 538 litres
(C) 740 litres
(D) 400 litres
Answer : A

Question. Read the statement carefully and write ‘T’ for true and ‘F’ for false.
(i) Volume of a cylinder is three times the volume of a cone on the same base and of same height.
(ii) Volume of biggest sphere in cube of edge 6 cm is 36p cm³.
(iii) Cuboids and cubes are special forms of right prisms.
      (i)      (ii)      (iii)
(A) T        F        T
(B) T        T        T
(C) F        T        F
(D) F        T        T
Answer : B

Question. The internal and external radii of a hollow hemispherical bowl are 15 cm and 16 cm respectively, find the cost of painting the bowl at the rate of 35 paise per cm2, if
(i) the area of the edge of the bowl is ignored.
(ii) the area of the edge of the bowl is taken into account.
              (i)             (ii)
(A) ₹ 1058.20     ₹ 1092.30
(B) ₹ 1020.50     ₹ 1045
(C) ₹ 1092.50     ₹ 1058.20
(D) ₹ 1086.20     ₹ 1095.2
Answer : A

Question. A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of the water is raised by 6.75 cm.
What is the radius of the sphere?
(A) 9 cm
(B) 13 cm
(C) 11 cm
(D) 15 cm
Answer : A

Question. Study the statements carefully.
Statement-I : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
Statement-II : Curved surface area is increased when diameter decreases.
Which of the following options hold?
(A) Both Statement-I and Statement-II are true.
(B) Statement-I is true but Statement-II is false.
(C) Statement-I is false but Statement-II is true.
(D) Both Statement-I and Statement-II are false.
Answer : B
 

Question. By stating the formula for the volume of cone as v= 1/3πl²h-1/3πh³ the following value is depicted.

(a) Truth value                               (b) Social value

(c) Respect for other views          (d) Equality

Question. 50 students of class X planned a visit to an old age home and to spend the whole day with its inmates. Each one prepared a cylindrical flower vase using cardboard to gift the inmates. The radius of cylinder is 4.2 cm and the height is 11.2 cm.

If the height of the cylinder is 21cm then

                                                                   

(a) What is the value of ‘a’ ?

 

(b) What is the curved surface area of a sphere ?

 

(c) Which value is shown by Ashwani ?

 

Answer: (a) diameter os sphere = height of cylinder

 

2a + 5 = 21

 

2a = 21–5 = 16

 

a = 8

 

(b) CSA of sphere = 4πr² 

 

=4× 22/7× 21/7× 21/7

 

= 1386 cm²

 

(c) Social justice, caring

 

Question. A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, a group of people decided to do WATER HARVESTING. They constructed a water reserviour measuring 48m × 27m × 25mto collect the rain water 

 

(a) For how many days the water of this tank is sufficient if during rain the height of water level is 5m.

 

(b) Which value is shown by the group of people ?

 

Answer: (a) Total volume of water = (48 × 27 × 5) m³

 

= 48×27×5×1000 litres

 

Requirement of water for one day = 5400 × 60 litres

 

No. of days = 48× 27× 5 ×1000/5400× 60

 

= 20 days

 

(b) environmental value, co-operation

 

Question. The patients in a hospital are given soup daily in a cylindrical bowl of diameter 7cm. On a particular day, the girls of KANYA MAHAVIDYALAYA decided to cook the soup for the patients. If they fill the bowl with soup to a height of 5cm then how much soup is to be cooked for 300 patients ? Which value is depicted by the girls ?

 

Answer: (a) Volume of the cylinder = πr2h

 

=π × (2/ 7)²× 5

 

=22/2× 7/2× 7/2 ×5

 

= 385 cm³

 

volume for 300 patients = 385/2× 300

 

= 57750 cm³

 

= 57.750 litres

 

(b) Social cohension, happiness

 

Question. The resident of society decided to paint the hall of cancer detective centre in their premises. If the floor of the cuboidal hall has a perimeter equal to 250 m and height 6m then

(a) Find the cost of painting its four walls (including doors etc) at the rate of Rs. 8 per m².

 

(b) What is the amount contributed by 50 people ?

 

(c) Which value is depicted by the residents ?

 

​​​​​​​Answer: P = 2(l+b) = 250

 

= l + b = 125

 

(a) Surface area of four walls = 2h (l+b)

 

= 6 × 250

 

= 1500 m²

 

cost = 8 × 1500

 

= Rs. 12000

 

(b) Amount contributed = Rs. 240

 

(c) Social value, co-operation, social cohension

 

Question. Sunidhi is curious to find out the relationship between the diameter of the moon and the earth. From the data available, it is known that the volume of earth is 64 times the volume of themoon. She concluded that the diameter of the moon is 1 /4 of the diameter of the earth.

 

(a) Justify her statement by proving it.

 

(b) Which value is depicted by Sunidhi by conducting the experiment?

 

​​​​​​​Answer: (a) Volume of earth = 64 × volume of moon

 

4/3πR₁³=64 ×4/3πR₂³

 

=R₁³=(4R₂)³

 

Radius of earth = 4 × Radius of moon

 

=1/4 Diameter of earth = Diameter of moon

 

(b) Curiosity, spirit of enquiry, scientific temper

 

Question. There are 100 students in a blind school. Mr. andMrs. Ramesh wished to serve them milk. They have two options for serving the milk. Option A – A hemispherical bowl with radius 10.5 cm made up of ecofriendly material. Option B – A hemispherical bowl with radius 7 cm made up of

plastic.

 

(a) How many litres of milk is required if option A is taken.

 

(b) Find the total quantity of milk (in litres) if option B is taken.

 

(c) Mr. and Mrs. Ramesh opted for option A which value is shown by them.

Answer: (a) r = 10.5 cm

 

volume of hemisphere = 2/3 π r³

 

Total volume = 2.42 × 100 = 242 l

 

(b) volume of hemisphere = 2 π r³

 

= 2/3× 22/7× 7× 7× 7

 

= 718.6 cm³

 

= 0.719 l

 

Total volume = 100 × 0.719 = 71.9 l

 

(c) Environmental value, social value