Answer:
Percentage decrease in surface area = [tex]19\%[/tex]
Step-by-step 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) = [tex]2\pi r(r+h)[/tex]
[tex]=2\pi (6)(6+4)\\=12\pi (10)\\=120 \pi\,\,cubic\,\,inches[/tex]
New radius of cylinder (R) = [tex]6-\frac{10}{100}(6)=6-0.6=5.4[/tex] inches
New height of cylinder (H) = [tex]4-\frac{10}{100}(4) =4-0.4=3.6[/tex]
New surface area of cylinder (A) = [tex]2\pi R(R+H)[/tex]
[tex]=2\pi(5.4)(5.4+3.6)\\=10.8\pi (9)\\=97.2\,\pi\,\,cubic \,\,inches[/tex]
Decrease in surface area = [tex]a-A=120\pi-97.2\pi=22.8\pi[/tex]
Percentage decrease in surface area = [tex]\frac{22.8\pi}{120\pi} (100)=19\%[/tex]
