# 6.03 Review: Surface area and volume of cylinders

Lesson

## Surface area of cylinders

We have learned how to calculate the surface area of a cylinder.

Recall that:

• Surface area of a cylinder is made up of two circles and one rectangle
• The radius of the circles is $r$r
• The width of the rectangle is $h$h
• The length of the rectangle is the circumference of the circle which is $2\pi r$2πr

Surface area of a cylinder formula

$\text{Surface Area of a Cylinder }=2\pi r^2+2\pi rh$Surface Area of a Cylinder =2πr2+2πrh

Let's try a few practice questions that require us to find the surface area of a cylinder.

#### Practice questions

##### QUESTION 1

Consider the following cylinder with a height of $105$105 mm and base radius of $28$28 mm. Find the total surface area.  Use the pi button on your calculator for pi.

1. Give your answer correct to $2$2 decimal places.

##### Question 2

Find the surface area of the cylinder shown, correct to 2 decimal places.  Use the pi button on your calculator for pi.

##### QUESTION 3 (extension)

A cylindrical can of radius $6$6 cm and height $10$10 cm is open at one end. What is the external surface area of the can correct to two decimal places?  Use the pi button on your calculator for pi.

## Volume of cylinders

We have already seen how the volume of a cylinder can be calculated in the same way that we calculate the volume of a rectangular prism, by using the rule

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

We just need to consider that the base of a cylinder is a circle (instead of a rectangle).

Volume of a cylinder formula
 $\text{Volume of Cylinder }$Volume of Cylinder $=$= $\text{Area of Base }\times\text{Height of Prism }$Area of Base ×Height of Prism $\text{Volume of Cylinder }$Volume of Cylinder $=$= $\pi r^2\times h$πr2×h $\text{Volume of Cylinder }$Volume of Cylinder $=$= $\pi r^2h$πr2h

Let's try some practice questions finding the volume of a cylinder using the formula.

#### Practice questions

##### QUESTION 4

The volume of a cylinder equals to:$V=\pi\times r^2\times h$V=π×r2×h.

Find the volume of the cylinder shown, correct to 2 decimal places.  Use the pi button on your calculator for pi.

##### QUESTION 5

Find the volume of a cylinder with radius $6$6 cm and height $14$14 cm, correct to 2 decimal places.  Use the pi button on your calculator for pi.

##### QUESTION 6

Consider the halfpipe with a diameter of $7$7 cm and a height of $16$16 cm.  Use the pi button on your calculator for pi.

1. Find its volume, rounding to 2 decimal places.