Measurement

Lesson

We have already seen how the volume of prisms can be calculated using the rule $\text{Volume }=\text{Area of Base }\times\text{Height of Prism }$Volume =Area of Base ×Height of Prism

(If you would like to refresh these topics try these pages, here and here)

A cylinder is very similar to a prism (except for the curved face), but the volume can be found using the same process we have already learnt.

$\text{Volume of Cylinder }=\text{Area of Base }\times\text{Height of Prism }$Volume of Cylinder =Area of Base ×Height of Prism

$\text{Volume of Cylinder }=\pi r^2\times h$Volume of Cylinder =π`r`2×`h`

$\text{Volume of Cylinder }=\pi r^2h$Volume of Cylinder =π`r`2`h`

You are at the local hardware store to buy a can of paint. After settling on one product, the salesman offers to sell you a can that is either double the height or double the radius (your choice) of the one you had decided on for double the price. Assuming all cans of paint are filled to the brim, is it worth taking up his offer?

If so, would you get more paint for each dollar if you chose the can that was double the radius or the can that was double the height?

Since the volume of a cylinder is given by the formula $\pi r^2h$π`r`2`h`, if the height doubles, the volume becomes $\pi r^2\times2h=2\pi r^2h$π`r`2×2`h`=2π`r`2`h` (ie the volume increases two-fold).

Whereas if the radius doubles, the volume becomes $\pi\left(2r\right)^2h=4\pi r^2h$π(2`r`)2`h`=4π`r`2`h` (ie the volume increases four-fold).

That is, the volume increases by double the amount when the radius is doubled compared to when the height is doubled.

To see how changes in height and radius affect the volume of a can to different extents, try the following interactive. You can vary the height and radius by moving the sliders around.

Find the volume of a cylinder correct to 1 decimal place if its diameter is $2$2 cm and its height is $19$19 cm.

Find the volume of a cylinder with radius $7$7 cm and height $15$15 cm, correct to 2 decimal places.

Calculate the volume of the solid correct to two decimal places.