Hasan is painting a spherical model of a human cell for his science class. He uses 100π square inches of paint (in one coat) to evenly cover the outside of the cell. What is the diameter of Hasan’s cell model?A) 2.5 in.B) 5.0 in.C) 10.0 in.D) 25.0 in.E) 50.0 in.
Accepted Solution
A:
Answer:10 inStep-by-step explanation:So we want to consider the surface area of this sphere. The formula for surface area of a sphere is [tex]A=4 \pi r^2[/tex].So we have that the surface area is [tex]100 \pi[/tex].So I'm going to replace [tex]A[/tex] in [tex]A=4 \pi r^2[/tex] with [tex]100 \pi[/tex].[tex]100\pi=4\pi r^2[/tex]Now our main objective here is to solve for [tex]r[/tex]:Divide both sides by [tex]4 \pi[/tex]:[tex]\frac{100\pi}{4 \pi}=\frac{4\pi r^2}{4 \pi}[/tex]This gets us [tex]r^2[/tex] by itself:[tex]25=r^2[/tex]What number squared gives you 25? If you don't know, just take the square root of both sides giving you:[tex]\sqrt{25}=r[/tex]Now you can just put [tex]\sqrt{25}[/tex] in your calculator. You should get 5.5 is the radiusThe diameter is twice the radius.So 2(5) is 10, so the diameter is 10 in.