Question

A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. find the diameter of the base of the cone.

Answer 1

Answer:

12.6 cm

Step-by-step explanation:

Diameter of Sphere = 12.6 cm

Radius of Sphere = $\frac{Diameter}{2} =\frac{12.6}{2} = 6.3$

Volume of sphere = $\frac{4}{3} \pi r^3$

                               = $\frac{4}{3} \pi \times (6.3)^3$

Height of cone= 25.2 cm

Volume of cone = $\frac{1}{3} \pi r^{2} h$

                          = $\frac{1}{3} \pi r^{2} (25.2)$

Since we are given that the sphere is melted and cast into cone So, volume will remain same.

So,  $\frac{4}{3} \pi \times (6.3)^3=\frac{1}{3} \pi r^{2} (25.2)$

$4\times (6.3)^3=r^{2} (25.2)$

$\frac{1000.188}{25.2}=r^{2}$

$39.69=r^{2}$

$\sqrt{39.69} = r$

$6.3 = r$

Thus the radius of cone is 6.3 cm

Diameter =$2 \times Radius = 2 \times 6.3 = 12.6 cm$

Hence the diameter of the cone is 12.6 cm