Question

Work out the surface area of the cylinder shown below.

Give your answer to 1 d.p.
30 mm circle diameter
36 mm cylinder length wise

Answer 1

We are given a cylinder of diameter 30mm i.e. radius 15mm and length equal to 36 mm. In order to find it's surface area ,we are required to find out the area of two circular bases and the area of the curved surface area and add the Resultant .

The area of circular base is given by

• πr^2 = 3.14*15mm*15mm = 706.5mm^2

since there are two bases thus,

• 706.5mm^2 x 2 = 1,413mm^2

And,

The curved surface area is given by

• 2πrh = 2*3.14*15mm*36mm = 3,391.2mm^2

Thus, the surface area of the cylinder would be

• 1,413mm^2 + 3,391.2mm^2 = 4,804.2mm^2

Therefore, 4,804.2mm^2 is the required surface area.

Answer 2

4806.6 mm³

Explanation:

The formula for the surface area of a cylinder is:

`\large\boxed{S.A.=2\pi r^2 + 2\pi r h}`

where:

• r is the radius of the circular base of the cylinder.
• h is the height of the cylinder.

Since the diameter of a circle is twice its radius, and the diameter of the circular base is 30 mm, then:

`r = (d)/(2)=(30)/(2)=15\; \sf mm`

The height of the cylinder is the given length. Therefore:

`h = 36\; \sf mm`

To calculate the surface area of the cylinder, substitute r = 15 and h = 36 into the surface area formula:

`S.A.=2\pi (15)^2 + 2\pi (15)(36)`

`S.A.=2\pi (225) + 2\pi (15)(36)`

`S.A.=450\pi + 1080\pi`

`S.A.=1530\pi`

`S.A.=4806.636759992...`

`S.A.=4806.6\; \sf mm^3\; (1\;d.p.)`

Therefore, the surface area of the cylinder is 4806.6 mm³, rounded to one decimal place.