Solve both Question related to Volume of Solids. 50 Points

Question

asked Apr 10, 2023 22.7k views

1 Answer

Galeop · Answer 1 · 2023-04-15T17:13:57+0000

Given for the cone:

given for the spheres:

Find volume of cone:

$\sf \hookrightarrow (1)/(3) \pi r^2h$

$\sf \hookrightarrow (1)/(3) \pi (3a)^2(4a)$

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

Find volume of sphere:

$\sf \hookrightarrow (4)/(3) \pi r^3$

$\sf \hookrightarrow (4)/(3) \pi a^3$

Divide volume of cone by volume of sphere:

$\sf \hookrightarrow (12\pi a^3)/( (4)/(3) \pi a^3)$

$\rightarrow 9$

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

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

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

$\sf \rightarrow a^3 = (12936)/(12\pi)$

$\sf \rightarrow a = \sqrt[3]{(12936)/(12\pi)}$

$\sf \rightarrow a =7$

Therefore the radius of sphere is 7 cm