Question

Two similar cylinders have heights 6 inches and 10 inches.

What is the ratio of their surface areas?

3 : 5

9 : 25

1 : 4

9 : 10

Answer 1

The total surface area of a cylinder is the lateral surface plus the area of the two bases.
A = 2(pi)rh + 2(pi)r^2
In you case for the one with height 6:
A6 = 2(pi)r(6) + 2(pi)r^2
For the one with height 10
A10 = 2(pi)r(10) + 2(pi)r^2
The ratio (sfter simplifying is
A6/A10 = [12(pi)r + 2(pi)r^2] / [20(pi)r + 2(pi)r^2]
Now you can factor out 2, r, and pi from both the numerator and denominator
A6/A10 = [2(pi)r (6 + r)] / [2(pi)r(10 + r)]
The 2(pi)r cancels out, and you're left with
A6/A10 = (r + 6)/(r + 10)

Answer 2

what? so how do i get the answer?

Answer 3

I see this is not a choice. That means your problem wants only the lateral area without the bases. I'll do it next.

Answer 4

would the answer be 3:5? cuz half of 6 and 10 are 2 and 5

Answer 5

Lateral area is 2(pi)rh
A6 = 2(pi)r(6) = 12(pi)r
A10 = 2(pi)r(10) = 20(pi)r

A6/A10 = [12(pi)r]/{20(pi)r]
pi and r cancels out
A6/A10 = 12/20 which reduces to 3/5

Answer 6

You are correct, 3:5

Answer 7

ok thank you! :)