# 10th Maths Chapter 7 Mensuration Exercise 7.5

10th Standard Maths Chapter 7 Mensuration Exercise 7.5 Guide. TN SSLC Samacheer Kalvi Guide Chapter 7 Exercise 7.5 Book Back Answers & Solutions. 10th All Subject Guide – Click Here. Class 1 to 12 All Subject Book Back Answers – Click Here.

### Multiple choice questions:

1. The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is ______
(1) 60π cm2
(2) 68π cm2
(3) 120π cm2
(4) 136π cm2
(4) 136π cm2
Hint:

2. If two solid hemispheres of the same base radius r units are joined together along with their bases, then the curved surface area of this new solid is
(1) 4πr2 sq. units
(2) 67πr2 sq. units
(3) 3πr2 sq. units
(4) 8πr2 sq. units
Solution:
(1) 47πr2 sq. units]

3.The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be __________
(1) 12 cm
(2) 10 cm
(3) 13 cm
(4) 5 cm
(1) 12 cm
Hint:

4. If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is
(1) 1 : 2
(2) 1 : 4
(3) 1 : 6
(4) 1 : 8
Solution:
(2) 1 : 4

5. The total surface area of a cylinder whose radius is 13 of its height is

Solution:
(3) 8πh2/9 sq. units

6. In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is _______
(1) 560π cm3
(2) 1120π cm3
(3) 56π cm3
(4) 360π cm3
(2) 1120π cm3
Hint:
R + r = 14 cm
w = 4 cm
h = 90 cm

7. If the radius of the base of a cone is tripled and the height is doubled then the volume is
(4) unchanged
Solution:
Hint:

8. The total surface area of a hemisphere is how many times the square of its radius ______
(1) π
(2) 4π
(3) 3π
(4) 2π
(3) 3π
Hint:

9. A solid sphere of radius x cm is melted and cast into a shape of a solid cone of the same radius. The height of the cone is
(1) 3x cm
(2) x cm
(3) 4x cm
(4) 2x cm
Solution:
(3) 4x cm
Hint:

10. A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is _______
(1) 3328π cm3
(2) 3228π cm3
(3) 3240π cm3
(4) 3340π cm3
(1) 3328π cm3Hint:

11. A shuttlecock used for playing badminton has the shape of the combination of
(1) a cylinder and a sphere
(2) a hemisphere and a cone
(3) a sphere and a cone
(4) frustum of a cone and a hemisphere
Solution:
(4) frustum of a cone and a hemisphere

12. A spherical ball of radius r1 units is melted to make 8 new identical balls each of radius r2 units. Then r1 : r2 is
(1) 2 : 1
(2) 1 : 2
(3) 4 : 1
(4) 1 : 4
Solution:
Hint:

#### 13. The volume (in cm3) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

(1) 4/3π
(2) 10/3π
(3) 5π
(4) 20/3π

Solution:
(1) 4/3π

14. The height and radius of the cone of which the frustum is a part are h1 units and r1 units respectively. Height of the frustum is h2 units and the radius of the smaller base is r2 units. If h2: h1 = 1 : 2 then r2 : r1 is
(1) 1 : 3
(2) 1 : 2
(3) 2 : 1
(4) 3 : 1
Solution:
(2) 1 : 2

15. The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is ____
(1) 1 : 2 : 3
(2) 2 : 1 : 3
(3) 1 : 3 : 2
(4) 3 : 1 : 2
(4) 3 : 1 : 2
Hint:

Solution:

### 2. A hemi-spherical tank of radius 1.75 m is full of water. It is connected with a pipe which empties the tank at the rate of 7 litre per second. How much time will it take to empty the tank completely?

Solution:
Suppose the pipe takes x seconds to empty the tank. Then, volume of the water that flows out of the tank in x seconds = Volume of the hemispherical tank.
Volume of the water that flows out of the tank in x seconds.
= Volume of hemispherical shell of radius 175 cm.

### 3. Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r units.

Solution:
Radius of the base of cone = Radius of the hemisphere = r
Height of the cone = Radius of the hemisphere

### 4. An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion be 8cm and the diameter of the top of the funnel be 18 cm, then find the area of the tin sheet required to make the funnel.

Solution:
Slant height of the frustum

### 5. Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

Solution:
No. of coins required.

### 6. A hollow metallic cylinder whose external radius is 4.3 cm and internal radius is 1.1 cm

and whole length is 4 cm is melted and recast into a solid cylinder of 12 cm long. Find the diameter of solid cylinder.
Solution:
Volume of the solid cylinder = Volume of the hollow cylinder melted.

Solution:

Solution:

Solution:

Solution: