Question

This is the last one i swear

Answer 1

`v=756\pi cm^(3)`

Explanation:

The radio of the cone:

`270=(1)/(3) r^(2) (10)`

`r^(2) =(3(270))/(10) =810/10`

`r^(2) =81`

`r=√(81) =9`

The half sphere (has the same radio):

`v=(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

Answer 2

V = 756π cm³

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

`(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 =
`√(81)` = 9

Volume of semi sphere =
`(2)/(3)` πr³

=
`(2)/(3)` π × 9³

=
`(2)/(3)` π × 729

= 2π × 243

= 486π

The volume (V) of the solid shape

V = 270π + 486π = 756π cm³