CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set 04

Objective Type Questions: 

Question. Choose and write the correct option in each of the following questions.
(i) The radius of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
(a) 2.1 cm
(b) 4.2 cm
(c) 3.1 cm
(d) 2.2 cm
Answer: (a) 2.1 cm

 

Question. A cylinder and a cone are of the same base radius and same height. The ratio of the volumes of the cylinder to that of the cone is
(a) 1 : 3
(b) 1 : 2
(c) 3 : 1
(d) 2 : 1
Answer: (c) 3 : 1

 

Question. The length of the diagonal of a cube is \( 8\sqrt{3} \text{ cm} \). Its total surface area is
(a) \( 321 \text{ cm}^2 \)
(b) \( 350 \text{ cm}^2 \)
(c) \( 384 \text{ cm}^2 \)
(d) \( 256 \text{ cm}^2 \)
Answer: (c) \( 384 \text{ cm}^2 \)

 

Question. If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5 cm and height 6 cm, then how much water flows out of the cylindrical cup? 
(a) \( 38.8 \text{ cm}^3 \)
(b) \( 55.4 \text{ cm}^3 \)
(c) \( 19.4 \text{ cm}^3 \)
(d) \( 471.4 \text{ cm}^3 \)
Answer: (a) \( 38.8 \text{ cm}^3 \)

 

Very Short Answer Questions: 

 

Question. Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas.
Answer: \( \frac{1}{9} \)

 

Question. A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3:4. 
Answer: The ratio is 3 : 4.

 

Question. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is \( 4\pi rh + 2\pi r^2 \). State true or false and justify. 
Answer: True

 

Question. The surface area of a sphere is \( 616 \text{ cm}^2 \). Find its radius. 
Answer: 7 cm

 

Question. The radii of two cylinders are in the ratio 2 : 5 and their heights are in the ratio 3 : 4. What is the ratio of their curved surface areas?
Answer: 3 : 10

 

Short Answer Questions-I: 

 

Question. A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surface areas?
Answer: \( \sqrt{2} : 1 \)

 

Question. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Answer: 100 minutes or 1 hour 40 minutes

 

Question. Two identical cubes of volume \( 343 \text{ cm}^3 \) are joined together end to end. What is the surface area of the resulting cuboid?
Answer: \( 490 \text{ cm}^2 \)

 

Question. Two cones with same base diameter 14 cm and height 24 cm are joined together along their bases. Find the surface area of the shape so formed.
Answer: \( 1100 \text{ cm}^2 \)

 

Question. A cone of maximum size is carved out from a cube of edge 20 cm. Find the surface area of the solid left out after the cone is carved out.
Answer: \( 2400 - \frac{2200}{7}(1 - \sqrt{5}) \text{ cm}^2 \)

 

Short Answer Questions-II:

 

Question. Find the number of shots, each having diameter 6 cm that can be made from a cuboidal lead which is solid of dimensions \( 24 \text{ cm} \times 22 \text{ cm} \times 12 \text{ cm} \).
Answer: 56

 

Question. Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker, so that the water level rises by 5.6 cm.
Answer: 150

 

Question. A wall 24 m long, 0.4 m thick and 6 m high which is constructed with the bricks, each of dimensions \( 25 \text{ cm} \times 16 \text{ cm} \times 10 \text{ cm} \). If the mortar occupies \( \frac{1}{10} \text{th} \) of the volume of the wall, then find the number of bricks used in constructing the wall. 
Answer: 12960

 

 

Question. A solid sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much height will the level of water rise in the cylindrical vessel? 
Answer: 1 cm

 

Question. A hemispherical tank full of water is emptied by a pipe at the rate of \( 3\frac{4}{7} \) litres per second. How much time will it take to empty the tank, if it is 3 m in diameter? \( \left( \text{Take } \pi = \frac{22}{7} \right) \) 
Answer: 1980 seconds or 33 minutes

 

Question. Two cones with same base diameter 16 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed. 
Answer: \( 854.08 \text{ cm}^2 \)

 

Long Answer Questions: 

 

Question. A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment. 
Answer: 10 m

 

Question. A factory manufactures 18000 cylindrical boxes daily. The length of each box is 32 cm and circumference of base is 6 cm. Find the cost of colouring the curved surfaces of the boxes manufactured in one day at Rs. 0.08 per \( \text{dm}^2 \).
Answer: Rs. 2764.80

 

Question. How many cubic centimeter of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm? If one cubic cm of iron weighs 7.5 g, find the weight of the box. 
Answer: \( 3960 \text{ cm}^3 \), 29.7 kg

 

Question. A well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment.
Answer: 0.7875 m

 

Question. A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.
Answer: \( 770 \text{ cm}^2 \)

 

Question. The interior of a building is in the form of a cylinder of diameter 4 m and height 3.5 m, surmounted by a cone of the same base with vertical angle as a right angle. Find the curved surface area and volume of the interior of the building.
Answer: \( (14 + 4\sqrt{2})\pi \text{ m}^2 \), \( \frac{50\pi}{3} \text{ m}^3 \)

 

Question. A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 9 cm and 15 cm, respectively. If the slant height of the conical portion is 7.5 cm, find the total surface area and volume of the rocket. 
Answer: \( 594 \text{ cm}^2 \), \( 1081.9 \text{ cm}^3 \)

 

Question. A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains \( 54 \frac{10}{21} \text{ m}^3 \) of air. If the internal diameter of dome is equal to \( \frac{4}{5} \) of the total height above the floor, find the height of the building.
Answer: 7.5 m

 

Question. Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/ sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?
Answer: 90 cm

 

Question. From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. \( \left[ \text{Take } \pi = \frac{22}{7} \right] \) 
Answer: \( 73.92 \text{ cm}^2 \)

 

Please click on below link to download CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set D