Question

A right circular cylinder has a radius of 6 inches and a height of 4 inches. Decrease the height and radius by 10% each, then find the percent change in surface are given the equation for the surface area of a cylinder is:

SA = 2(pi)rh + 2(pi)r^2

Answer 1

Percentage decrease in surface area =
`19\%`

Explanation:

Given: A right circular cylinder has a radius of 6 inches and a height of 4 inches.

To find: percent change in surface area of the cylinder if height and radius are decreased by 10%

Solution:

Original radius of cylinder (r) = 6 inches

Original height of cylinder (h) = 4 inches

Original surface area of cylinder (a) =
`2\pi r(r+h)`

`=2\pi (6)(6+4)\\=12\pi (10)\\=120 \pi\,\,cubic\,\,inches`

New radius of cylinder (R) =
`6-(10)/(100)(6)=6-0.6=5.4` inches

New height of cylinder (H) =
`4-(10)/(100)(4) =4-0.4=3.6`

New surface area of cylinder (A) =
`2\pi R(R+H)`

`=2\pi(5.4)(5.4+3.6)\\=10.8\pi (9)\\=97.2\,\pi\,\,cubic \,\,inches`

Decrease in surface area =
`a-A=120\pi-97.2\pi=22.8\pi`

Percentage decrease in surface area =
`(22.8\pi)/(120\pi) (100)=19\%`