Question

The inner circumference of a hollow cylindrical pipe is 4.5 metres and outer circumference is 4.6 metres. Find the cost of painting both its inner and outer sides at the rate of 20 per metre square, if it is 8 metres tall.

Answer 1

`\$527.2`

Explanation:

`r_i` = Inner radius

Inner circumference = 4.5 m

`2\pi r_i=4.5\\\Rightarrow r_i=(4.5)/(2\pi)\\\Rightarrow r_i=(2.25)/(\pi)`

`r_o` = Outer radius

Outer circumference = 4.6 m

`2\pi r_o=4.6\\\Rightarrow r_o=(4.6)/(2\pi)\\\Rightarrow r_o=(2.3)/(\pi)`

h = Height of cylindrical pipe = 8 m

Total surface area to be painted

`s=\pi r_i^2h+\pi r_o^2h\\\Rightarrow s=\pi h(r_i^2+r_o^2)\\\Rightarrow s=\pi* 8(((2.25)/(\pi))^2+((2.3)/(\pi))^2)\\\Rightarrow s=26.36\ \text{m}^2`

Cost of painting 1 square meter is 20

Cost of painting the inner and outer surfaces is
`20* 26.36=\$527.2`

The total cost painting the surfaces is
`\$527.2`.