Question

Work out the volume of the shape​

Answer 1

`\large\boxed{V=504\pi\ cm^3}`

Explanation:

We have the cylinder and the half-sphere.

The formula of a volume of a cylinder:

`V_c=\pi r^2H`

r - radius

H - height

We have r = 6cm and H = 10cm.

Substitute:

`V_c=\pi(6^2)(10)=\pi(36)(10)=360\pi\ 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 is:

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

We have R = 6cm. Substitute:

`V_(hs)=(2)/(3)\pi(6^3)=(2)/(3)\pi(216)=(2)/(1)\pi(72)=144\pi\ cm^3`

The volume of the given shape:

`V=V_c+V_(hs)`

Substitute:

`V=360\pi+144\pi=504\pi\ cm^3`