Question

Find the volume of the solid where the cone and half sphere are hollow. Use 3.14 for π.

Answer 1

Volume of Solids

The volume of the solid is 2813 in³

Explanation:

Given that the cone and half sphere is hollow

The volume of the cone
`=1/3\pi r^2h`

The Volume of the sphere
`=4/3\pi r^3`

So the Volume of the half sphere
`=2/3\pi r^3`

The volume of solid = volume of cone + volume of the half sphere

`V=V_1+V_2`

Given

height h = 26 in

radius r = 8 in

`V_1=1/3\pi r^2h`

`= 1/3 * 3.14 * 8 * 8* 26`

`=1741.65 \ in^3`

`V_2=2/3\pi r^3`

`= 2/3 * 3.14 * 8 * 8* 8`

`= 1071.78 \ in^3`

`V = 1741.65 \ in^3 + 1071.78 \ in^3`

`2813 \ in^3`

Hence the volume of the solid is 2813 in³

Answer 2

The Answer: 758.83 in³

Explanation:

Volume of Solids

The volume of the solid is 758.83 in³

Explanation:

Given that the cone and half sphere is hollow

The volume of the cone =

The Volume of the sphere =

So the Volume of the half sphere =

The volume of solid = volume of cone + volume of the half sphere

Given

height h = 19 in

radius r = 5 in

=

= 1/3 × 3.14 × 5 × 5 × 19

= 497.16 in³

= 2/3 × 3.14 × 5 × 5 × 5

= 261.67 in³

V = 497.16 in³ + 261.67 in³

= 758.83 in³

Hence the volume of the solid is 758.83 in³