 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.