Volume and Surface Area of a Cylinder

The objective of this section is to

Volume of prism = area of cross-section × length
= Al

A cylinder is a prism with a circular cross-section.

Volume of cylinder = A × h
= πr2h

The total surface area of the cylinder can be determined by splitting it into 3 parts as below:

The curved surface can be opened out to form a rectangle. The length of one side is equal to the height, h, of the cylinder; the other is equal to the circumference of the cross-section, 2πr .

Total area = area of curved surface + area of top + area of bottom
= 2πrh + πr2 + πr2
= 2πrh + 2πr2
On this page, give your answers rounded to 3 s.f. where necessary.
1

Calculate the volume and surface area of the cylinder shown in the diagram.

Show

The radius of the base of the cylinder is 3 cm.

Volume = πr2h
= π × 32 × 8
= 226 cm3 (3 s.f.)
Surface area = 2πrh + 2πr2
= 2 × π × 3 × 8 + 2 × π × 32
= 207 cm2 (3 s.f.)
2

The diagram shows a sheet of card that is to be used to make the curved surface of a cylinder of height 8 cm.

(a)

Calculate the radius of the cylinder.

Show

The circumference of the cross-section is 22 cm, so

2πr = 22
r =
=
= 3.50 cm (3 s.f.)
(b)

Use your answer to part (a) to calculate the area of card that would be needed to make ends for the cylinder.

Show
Area of ends = 2 × πr2
= 2 × π × 3.502
= 77.0 cm2 (3 s.f.)
(c)

Calculate the volume of the cylinder.

Show
Volume of cylinder = πr2h
= π × 3.52 × 8
= 308 cm3 (3 s.f.)

Calculate the volume of the cylinder shown.

cm3

Look at the dimensions of the following cylinders:

(a)

Without doing any calculations, decide which cylinder you think has the greatest volume.

(b)

Determine the volume of each cylinder and see if you were correct.

A: cm3

B: cm3

C: cm3

Calculate the total surface area of the following cylinder:

Surface = cm2

The following diagrams show two cylinders, A and B:

(a)

Show that both cylinders have the same volume.

Volume of A = cm3

Volume of B = cm3

(b)

Calculate the total surface area of each cylinder.

Surface of A = cm2

Surface of B = cm2

A cylinder has volume 250 cm3 and base radius 6 cm.

(a)

Calculate the height of the cylinder.

cm
(b)

Calculate the total surface area of the cylinder.

cm2

A cylinder has volume 300 cm3 and height 9 cm. Calculate the diameter of the cylinder.

cm

The curved surface of a cylinder is to be made from a rectangular sheet of material which is 18 cm by 32 cm.

Explain why two different cylinders could be made from this sheet.

(a)

Calculate the radius of each of the cylinders.

r = cm or cm

(b)

Calculate the volume of each cylinder.

V = cm3 or cm3

A cylinder has height 11 cm. The area of the curved surface of the cylinder is 40 cm2 . Calculate the volume of the cylinder.

cm3

The diagram shows the cross-section of a clay pipe. The length of the pipe is 40 cm.

Calculate the volume of clay needed to make the pipe.

cm3

Calculate the volume and the total surface area of the shape shown.

Volume = cm3

Surface = cm2