Question

Work out the volume of the shape​

Answer 1

`\large\boxed{V=(1,421\pi)/(3)\ cm^3}`

Explanation:

We have the cone and the half-sphere.

The formula of a volume of a cone:

`V_c=(1)/(3)\pi r^2H`

r - radius

H - height

We have r = 7cm and H = (22-7)cm=15cm. Substitute:

`V_c=(1)/(3)\pi(7^2)(15)=(1)/(3)\pi(49)(15)=(735\pi)/(3)\ cm^3`

The formula of a volume of a sphere:

`V_s=(4)/(3)\pi R^3`

R - radius

Therefore the formula of a volume of a half-sphere:

`V_(hs)=(1)/(2)\cdot(4)/(3)\pi R^3=(2)/(3)\pi R^3`

We have R = 7cm. Substitute:

`V_(hs)=(2)/(3)\pi(7^3)=(2)/(3)\pi(343)=(686\pi)/(3)\ cm^3`

The volume of the given shape:

`V=V_c+V_(hs)`

Substitute:

`V=(735\pi)/(3)+(686\pi)/(3)=(1,421\pi)/(3)\ cm^3`