## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.2

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.2

Take π = \(\\ \frac { 22 }{ 7 } \) unless stated otherwise.

Question 1.

Write whether the following statements are true or false. Justify your answer.

(i) If the radius of a right circular cone is halved and its height is doubled, the volume will remain unchanged.

(ii) A cylinder and a right circular cone are having the same base radius and same height. The volume of the cylinder is three times the volume of the cone.

(iii) In a right circular cone, height, radius and slant height are always the sides of a right triangle.

Solution:

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Question 2.

Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.

Solution:

Question 3.

Diameter of the base of a cone is 10.5 cm and slant height is 10 cm. Find its curved surface area.

Solution:

Question 4.

Curved surface area of a cone is 308 cm^{2} and its slant height is 14 cm. Find

(i) radius of the base

(ii) total surface area of the cone.

Solution:

Question 5.

Find the volume of the right circular cone with

(i) radius 6 cm and height 7 cm

(ii) radius 3.5 cm and height 12 cm.

Solution:

Question 6.

Find the capacity in litres of a conical vessel with

(i) radius 7 cm, slant height 25 cm

(ii) height 12 cm, slant height 13 cm

Solution:

Question 7.

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kiloliters?

Solution:

Question 8.

If the volume of a right circular cone of height 9 cm is 48π cm^{3}, find the diameter of its base.

Solution:

Question 9.

The height of a cone is 15 cm. If its volume is 1570 cm^{3}, find the radius of the base. (Use π = 3.14)

Solution:

Question 10.

The slant height and a base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of whitewashing its curved surface area at the rate of Rs 210 per 100 m^{2}.

Solution:

Question 11.

A conical tent is 10 m high and the radius of its base is 24 m. Find:

(i) the slant height of the tent.

(ii) cost of the canvas required to make the tent, if the cost of 1 m^{2} canvas is Rs 70.

Solution:

Question 12.

A Jocker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the cloth required to make 10 such caps.

Solution:

Question 13.

(a) The ratio of the base radii of two right circular cones of the same height is 3 : 4. Find the ratio of their volumes.

(b) The ratio of the heights of two right circular cones is 5 : 2 and that of their base radii is 2 : 5. Find the ratio of their volumes.

(c) The height and the radius of the base of a right circular cone is half the corresponding height and radius of another bigger cone. Find:

(i) the ratio of their volumes.

(ii) the ratio of their lateral surface areas.

Solution:

Question 14.

Find what length of canvas 2 m in width is required to make a conical tent 20 m in diameter and 42 m in slant height allowing 10% for folds and the stitching. Also, find the cost of the canvas at the rate of Rs 80 per metre.

Solution:

Question 15.

The perimeter of the base of a cone is 44 cm and the slant height is 25 cm. Find the volume and the curved surface of the cone.

Solution:

Question 16.

The volume of a right circular cone is 9856 cm^{3} and the area of its base is 616 cm^{2}. Find

(i) the slant height of the cone.

(ii) the total surface area of the cone.

Solution:

Question 17.

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface of the cone so formed. (Take π = 3.14)

Solution:

Question 18.

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is \(\\ \frac { 1 }{ 27 } \) of the volume of the given cone, at what height above the base is the section cut?

Solution:

Question 19.

A semi-circular lamina of radius 35 cm is folded so that the two bounding radii are joined together to form a cone. Find

(i) the radius of the cone.

(ii) the (lateral) surface area of the cone.

Solution: