Geometry

Solids

Easy

The radii of two cones are in the ratio 2:3 and their volumes are in the ratio 1:3. Then the ratio of their heights is:

$3:2$

$1:2$

$3:4$

$2:3$

✅ Correct Option: 3

Let's use the formula for volume of a cone:

$V = \frac{1}{3}πr^2h$ , where $r$ is radius and $h$ is height

Given:

Ratio of radii $(r_1:r_2) = 2:3$ $(r_{1} : r_{2}) = 2 : 3$
- Ratio of volumes $(V_1:V_2) = 1:3$

Let's express volume ratio using formula:

$\frac{V_1}{V_2} = \frac{\frac{1}{3}πr_1^2h_1}{\frac{1}{3}πr_2^2h_2} = \frac{r_1^2h_1}{r_2^2h_2} = \frac{1}{3}$

Now substitute radius ratio:

If $\frac{r_1}{r_2} = \frac{2}{3}$ , then $\frac{r_1^2}{r_2^2} = \frac{4}{9}$

Put this in volume ratio equation:

$\frac{4}{9} × \frac{h_1}{h_2} = \frac{1}{3}$

Solve for height ratio:

$\frac{h_1}{h_2} = \frac{1}{3} × \frac{9}{4} = \frac{3}{4}$

Therefore, the ratio of heights $(h_1:h_2) = 3:4$

The answer is $3:4$ .

JIPMAT 2022

Floor of a room is $15 \text{ m } 17 \text{ cm}$ long and $9 \text{ m } 2 \text{ cm}$ broad. What is the least number of square tiles required to pave the floor?

JIPMAT 2024

If each side of a cube is decreased by $19 \%$ , then the decrease in surface area is :

JIPMAT 2023

A 30 meter deep well, with a diameter of 7 meters is dug and the earth from digging is evenly spread out to form a platform of size 22 meters by 14 meters. The height of the platform is:

JIPMAT 2026

The sum of length, breadth and height of a cuboid is 22 cm and length of its body diagonal is 14 cm. if S is the sum of cubes of dimensions of the cuboid and V is the volume, the (S−3V) will be equal to

JIPMAT 2026

The sum of length, breadth and height of a cuboid is 22 cm and the length of its body diagonal is 14 cm. What is the surface area of the cuboid?

JIPMAT 2025

A solid brass sphere of radius 21 cm is converted into a right circular cylindrical rod of length 28 cm. The ratio of total surface areas of the rod to sphere is :

The radii of two cones are in the ratio 2:3 and their volumes are in the ratio 1:3. Then the ratio of their heights is:

Solution

Related questions:

Keyboard Shortcuts

JIPMAT Past Year Questions (Topic-Wise)