Question

Surface Areas and Volume ​

Answer 1

3.3.1

A cylinder has a circular base.

3.3.2

As cylinders have circular bases, the formula for the area of the base of a cylinder should be the same as the formula for the area of a circle:

`\boxed{\mathrm{Area = \pi r^2}}`.

3.3.3

To find the volume of a cylinder, we can imagine stacking multiple circles on top of each other so that the height of the structure increases, and the shape becomes a cylinder.

This means that the volume of a cylinder is simply the area of the base circle multiplied by the height (h) of the cylinder.

∴
`\boxed{\mathrm{Volume = \pi r^2h}}`.

3.3.4

We can use the above formula to calculate the volume of the given cylinder, where:

• r =
`\mathrm{(diameter)/(2)}` =
`(8)/(2)` = 4 m

• h = 3 m

∴
`\mathrm{Volume = \pi * (4 \: m)^2 * 3 \: m}`

`= \mathrm{\pi * 16 \:m^2 * 3 \: m}`

`= \mathrm{48 \pi \: m^3 }`

`= \mathrm{\bf150.8 \space\ m^3}`