Question

Find the lateral surface area and the total surface area of the following cylinder i.Radius =21cm and height= 45cm

ii.Radius =28cm and height=28

Answer 1

Radius =21, height = 45
Lateral Surface Area =
`5937.61` cm²
Total Surface Area =
`8708.49` cm²

Radius = 28, height =28
Lateral Surface Area =
`4926.01` cm²

Total Surface Area =
`9852.03` cm²

Explanation:

If r is the radius of a cylinder with height h

Lateral surface area

`L = 2\pi rh`

Top and bottom surface area for each which is a circle is
`\pi r^2`

So total bottom and top surface area =
`2 \pi r^2`

Total surface area =

`2\pi rh + 2\pi r^2 = 2\pi r(h + r)`

For r = 21, h = 45

`L = 2 \pi \cdot 21 \cdot 45 = 1890 \pi = 5937.61 \;cm^2`

`T = 2\pi \cdot 21 (21 + 45) = 2772 \pi = 8708.4948\;cm^2`

For r = 28, h = 28

`L = 1568\pi = 4926.01 cm^2`

`T = 3136\pi = 9852.03 \;cm^2`