Question

A cylinder has a cross-section circumference of 56cm. The height of the cylinder is 3.2cm. Calculate the volume and surface area of the cylinder.

Answer 1

volume = 798.58 cm³ (nearest hundredth)

surface area = 678.31 cm³ (nearest hundredth)

Explanation:

Volume of a cylinder:
`V=\pi r^2h`

Surface area of a cylinder:
`SA=2\pi r^2+2\pi rh`

Circumference:
`C=2\pi r`

(where r is the radius and h is the height)

Given circumference = 56

⇒
`56 = 2\pi r`

⇒
`r=(56)/(2\pi )=(28)/(\pi )`

`V=\pi \left((28)/(\pi)\right)^2 *3.2=(2508.8)/(\pi)=798.58 \textsf{ cm}^3 \textsf{ (nearest hundredth)}`

`SA=2\pi \left((28)/(\pi)\right)^2+56 *3.2=(1568)/(\pi)+179.2=678.31 \textsf{ cm}^3 \textsf{ (nearest hundredth)}`