Page 149 - Cambridge+Checkpoint+Mathematics+Coursebook+9

15.4 Calculating with prisms and cylinders

A cylinder is also a prism. !e cross-section is a circle.
!e formula for the area of a circle is: A = πr 2
cross-section

!e formula for the volume of a prism is: volume = area of cross-section × length height (h)

So the formula for the volume of a cylinder is: volume = πr × height
2

or simply V = πr h
2

Worked example 15.4b
3 cm
a Work out: i the volume
ii the surface area of this cylinder. 8 cm
b A cylinder has volume 552.2 cm . The radius of the circular end is 5.2 cm.
3
What is the height of the cylinder? Give your answer in centimetres.

2
a i V = πr h Write down the formula for the volume of a cylinder.
= π × 3 × 8 Substitute the radius and height measurements in the formula.
2
= 226.2 cm Work out the answer and remember the units, cm .
3
3
2
ii Area of circle = πr Work out the area of one of the circular ends.
= π × 3 Substitute the radius measurement in the formula.
2
= 28.27 cm Write down the answer, correct to at least two decimal places.
2
C = 2πr The curved surface of a cylinder is a rectangle with length the
= 2 × π × 3 = 18.85 cm same as the circumference of the circle. Work this out first.
Area of rectangle = 18.85 × 8 Now work out the area of the curved surface (length × height).
2
= 150.80 cm Write down the answer, correct to at least two decimal places.
Total area = 2 × 28.27 + 150.80 Add together the area of the two ends and the curved surface.
2
= 207.3 cm Write down the final answer, correct to one decimal place.
b V = πr h Write down the formula for the volume of a cylinder.
2
2
552.2 = π × 5.2 × h Substitute the volume and radius in the formula.
552 2
.
h = 2 Rearrange the formula to make h the subject.
π × 52
.
= 6.5 cm Work out the answer and remember the units, cm.
) Exercise 15.4
1 Work out the volume of each prism.
a b c

8 cm 4.2 cm
6.5 cm
15 cm 2 32 cm 2
20 cm 2
2 Copy and complete this table.
Area of cross-section Length of prism Volume of prism

a 12 cm 2 10 cm cm 3
b 24 cm 2 cm 204 cm 3
c m 2 6.2 m 114.7 m 3

148 15 Area, perimeter and volume