Question

A solid cube of side 7 cm is melted to make a cone of height 5 cm, find the radius of the base of the cone.

Answer 1

hola there

Given,

Edge of cube, a = 7 cm

Volume of cube = a3

= (7)3

= 343 cm3

Height of cone, h = 5 cm

Let radius of the cone be r

Volume of cone = Volume of cube

1/3TTr2h = 343

1/3*22/7*r2*5 = 343

r2 = 65.482

r = 8.1 cm

Answer 2

Given:

A solid cube of side 7 cm is melted to make a cone of height 5 cm.

To find:

The radius of the base of the cone.

Solution:

As given, we have

side of solid cube = 7 cm

height of cone = 5 cm

Also,

As given, the solid cube is melted to make a cone so the volume of the solid cube and cone will be equal.

Hence,

the volume of solid cube = volume of a cone

${a}^{3} = \frac{1}{3} \pi {r}^{2} h$

where a = side of the cube, h = height of the cone and r = radius of the cone.

So,

on putting the given values, we have,

${(7)}^{3} = \frac{1}{3} \pi {r}^{2} 5$

$7 \times 7 \times 7 = \frac{1}{3} \times \frac{22}{7} \times {r}^{2} \times 5$

${r}^{2} = \frac{7 \times 7 \times 7 \times 7 \times 3}{22 \times 5}$

${r}^{2} = \frac{7 \times 7 \times 7 \times 7 \times 3}{110}$

on solving the above, we get

${r}^{2} = 65.481$

Taking square root on both sides, we have

$r = 8.1$

Hence, the radius of the base of the cone is 8.1cm.