Geometry

Solids

Medium

The heights of two right circular cones are in the ratio 1 : 2 and the circumferences of their bases are in the ratio 3 : 4. Find the ratio of their volumes.

32 : 9

9 : 32

7 : 23

23 : 7

✅ Correct Option: 2

Circumference ratio = radius ratio = 3:4. Volume $\propto r^2 h$ . Ratio = $3^2\times 1 : 4^2\times 2 = 9 : 32$ .

2022: 8 Aug Shift 1

A volume of a wall is 128 cm $^3$ . If the height of the wall is 6 times its breadth and the length is 9 times its breadth, find the breadth.

2025: 2 June Shift 2

A solid, metallic right circular cone of radius 7 cm and height 3 cm is melted into three cubes. If the sides of two cubes are 3 cm and 5 cm, then the side of the third cube will be how much?

2025: 2 June Shift 2

If the ratio of the radii of the sphere and hemisphere is √3:2, then determine the ratio of their total surface area?

2025: 15 May Shift 1

Match List-I with List-II

List-I	List-II
(Figures, etc.)	(Area/Volume/Diagonal etc.)
(A) Surface area of Cube	(I) $\pi(R^2 - r^2)$
(B) Volume of Right pyramid	(II) $a\sqrt{2}$
(C) Area of Circular Ring	(III) $6a^2$
(D) Diagonal of Square	(IV) $\frac{1}{3}$ (area of base) × height

Choose the correct answer from the options given below:

2023: 24 May Shift 3

A cuboidal slab of copper having dimensions 22 cm $\times$ 10 cm $\times$ 5 cm is melted and recasted in the form of a wire of 1 mm diameter. The wire is rubber coated at the rate of Rs. 1.50 per meter. Find the cost of rubber coating (in Rs.) Use $\pi = \frac{22}{7}$ .

2023: 19 June Shift 1

A cone of height 24 cm and base radius 6 cm is made of modelling clay. A child reshapes it in the form of a sphere. The radius of the sphere is :

The heights of two right circular cones are in the ratio 1 : 2 and the circumferences of their bases are in the ratio 3 : 4. Find the ratio of their volumes.

Solution

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