Question

A solid sphere of diameter 18 cm is melted and is recast into small identical cones of height 6 cm and radius of 6 cm. The number of cones formed is
a)24
b)32
c)12
d)18​

Answer 1

Given:

• Diameter of Solid Sphere = 18 cm
• Height of Cone = 6 cm
• Radius of Cone = 6 cm

Solution:

We know that, if a sphere is melted into different shapes the volume will be the same. Because the same volume is melted and recast to form a new shape.

So,

Volume of Sphere = Total volume of cones formed

$\dfrac{4}{3} \times \pi \times {(r_1)}^{3} =n\times \dfrac{1}{3} \times \pi \times {(r_2) }^{2} \times h$

Here,

Radius of Sphere = 9 cm.

n = number of cones formed

Substituting these values, we get:

$\large{☞}$$\dfrac{4}{3} \times {9}^{3} = n \times \dfrac{1}{3} \times {6}^{2} \times 6$

$\large{☞}$$n = \dfrac{4 \times 3}{3} \times \dfrac{729}{216}$

$\large{☞}$$n = \dfrac{81}{6}$

$\large{☞}$$n = 13.5$

So, the question has wrong input values as answer cannot be 13.5.

Formulas Used:

Volume of Sphere = $\dfrac{4}{3}\pi r^3$

Volume of Cone = $\dfrac{1}{3}\pi r^2 h$