Question

This is the last one i swear

Answer 1

Answer:

V = 756π cm³

Step-by-step explanation:

The solid shape consists of a cone and a semi sphere

To calculate the volume of the semi sphere we require to find its radius r

Given

volume of cone = 270π , then

$\frac{1}{3}$ πr²h = 270π ( multiply both sides by 3 to clear the fraction )

πr²h = 810π ( divide both sides by π )

r²h = 810

from diagram h = 10

10r² = 810 ( divide both sides by 10 )

r² = 81 ( take square root of both sides )

r = $\sqrt{81}$ = 9

Volume of semi sphere = $\frac{2}{3}$ πr³

                                       = $\frac{2}{3}$ π × 9³

                                       = $\frac{2}{3}$ π × 729

                                      = 2π × 243

                                      = 486π

The volume (V) of the solid shape

V = 270π + 486π = 756π cm³

Answer 2

Answer:

$v=756\pi cm^{3}$

Step-by-step explanation:

The radio of the cone:

$270=\frac{1}{3} r^{2} (10)$

$r^{2} =\frac{3(270)}{10} =810/10$

$r^{2} =81$

$r=\sqrt{81} =9$

The half sphere (has the same radio):

$v=\frac{2}{3} \pi (9)^{3} =486\pi$

The volume of the solid shape:

$v=270\pi +486\pi =756\pi cm^{3}$

Hope this helps