Question

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is
(a)12 cm
(b)24 cm
(c)30 cm
(d)36 cm

Answer 1

The volume of the new sphere will be equal to the combined volume of the three smaller spheres.

Let the radius of new sphere be r cm, then

4/3 πr^3 = 4/3 π(6^3 + 8^3 + 10^3)

⇨ r3 = 6^3 + 8^3 + 10^3

= 1728

r = 12 cm

Diameter = 2 * radius

= 2* 12

= 24 CM

The correct option is B.

Answer = 24

Answer 2

Given,

Radii of three metallic spheres are 6cm, 8cm and 10cm

Volume of Single Sphere = Volume of three spheres

$\frac{4}{3} \pi {r}^{3} = (\frac{4}{3} \pi {6}^{3} ) + ( \frac{4}{3} \pi {8}^{3} ) + ( \frac{4}{3} \pi {10}^{3} ) \\ \\ \frac{4}{3} \pi {r}^{3} = \frac{4}{3} \pi216 + \frac{4}{3} \pi512 + \frac{4}{3} \pi1000 \\ \\ \frac{4}{3} \pi {r}^{3} = \frac{4}{3} \pi(216 + 512 + 1000) \\ \\ \frac{4}{3}\pi {r}^{3} = \frac{4}{3} \pi(1728) \\ \\ {r}^{3} = 1728 \\ \\ r = \sqrt[3]{1728} \\ \\ r = 12cm$

Diameter = 12 × 2 = 24cm

Therefore, the diameter of new sphere is 24cm.