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RD Chapter 20 Surface Areas and Volume of A Right Circular Cone Ex 20.2 Solutions

Question - 1 : -
Find the volume of a right circular cone with:
(i) radius 6 cm, height 7 cm
(ii) radius 3.5 cm, height 12 cm
(iii) height 21 cm and slant height 28 cm. [NCERT]

Answer - 1 : -

(i) Radius of a cone (r) = 6 cm
and height (h) = 7 cm

Question - 2 : -
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. [NCERT]

Answer - 2 : -

(i) Radius of the conical vessel (r) = 7 cm
Slant height (h) = 25 cm

Question - 3 : - Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.

Answer - 3 : - Ratio in the heights of two cones =1:3
and ratio in their radii = 3: 1
Let radius of first cone (r1)= x
and of second cone (r2)= 3x
and height of first cone (h1)= 3y
and of second cone (h2)

Question - 4 : - The radius and the height of a right circular cone arein the ratio 5 : 12. If its volume is 314 cubic metre, find the slant heightand the radius (Use π = 3.14).

Answer - 4 : - Ratio in the radius and height of a cone = 5 : 12
Volume = 314 cm3
Let radius (r) = 5x
and height (h) = 12x

Question - 5 : - The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use π = 3.14).

Answer - 5 : - Ratio in the radius and height of a right circularcone = 5 : 12
Volume = 2512 cm3
Let radius (r) = 5x
Then height (h) = 12x

Question - 6 : - The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.

Answer - 6 : -

Ratio in volumes of two cones = 4:5
and ratio in radii = 2:3
Let radius of the first cone (r1) = 2x
Then radius of second cone (r2) = 3x
Let h1, h2 be their heights respectively

Question - 7 : - Ratio between their vertical heights = 9:5 7. A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.

Answer - 7 : - Let r be the radius and h be the height of a cylinderand a cone, then
Volume of cylinder = πr2h

Question - 8 : - If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?

Answer - 8 : - Let r be the radius and h be the height of the cone,then
Volume = πr2h

By halving the radius and same height the

Question - 9 : - A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π = 3.14). [NCERT]

Answer - 9 : - Diameter of conical heap of wheat = 9 m

Question - 10 : - Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm, supposing the material of which it is made weighs 10 grams per cubic cm.

Answer - 10 : -

Diameter of the base of solid cone = 14 cm
and vertical height (h) = 51 cm

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