Question

Solve both Question related to Volume of Solids. 50 Points​

Answer 1

Given for the cone:

• base radius: 3a

• perpendicular height: 4a

given for the spheres:

• radius: a

Find volume of cone:

$\sf \hookrightarrow \dfrac{1}{3} \pi r^2h$

$\sf \hookrightarrow \dfrac{1}{3} \pi (3a)^2(4a)$

$\sf \hookrightarrow 12\pi a^3$

Find volume of sphere:

$\sf \hookrightarrow \dfrac{4}{3} \pi r^3$

$\sf \hookrightarrow \dfrac{4}{3} \pi a^3$

Divide volume of cone by volume of sphere:

$\sf \hookrightarrow \dfrac{12\pi a^3}{ \dfrac{4}{3} \pi a^3}$

$\rightarrow 9$

Therefore proved 9 such spheres can be made using the metal cone.

We know that volume of cone is $12\pi a^3$

$\sf \rightarrow 12\pi a^3 = 12936$

$\sf \rightarrow a^3 = \dfrac{12936}{12\pi}$

$\sf \rightarrow a = \sqrt[3]{\dfrac{12936}{12\pi}}$

$\sf \rightarrow a =7$

Therefore the radius of sphere is 7 cm