Question
A cylinder has a surface area of 54π cm cm^2 . If it were dilated using a scale factor of 1/2 , what is the surface area of the new cylinder?(1 point)
Answers
GPT 3.5
The formula for the surface area of a cylinder is given by 2πr² + 2πrh, where r is the radius and h is the height.
Let's assume the radius of the original cylinder is r. Then, the surface area of the original cylinder is 2πr² + 2πrh = 54π cm².
If we dilate the cylinder with a scale factor of 1/2, the radius and height of the new cylinder will be half of the original. Let's denote the new radius as (1/2)r and the new height as (1/2)h.
The surface area of the new cylinder is then given by 2π[(1/2)r]² + 2π[(1/2)r][(1/2)h].
Simplifying this expression, we have π(1/4)r² + π(1/4)rh = (1/4)(2πr² + 2πrh) = (1/4)(54π) cm².
Therefore, the surface area of the new cylinder is (1/4)(54π) cm² = 54π/4 cm² = 13.5π cm². Answer: \boxed{13.5\pi}.
Let's assume the radius of the original cylinder is r. Then, the surface area of the original cylinder is 2πr² + 2πrh = 54π cm².
If we dilate the cylinder with a scale factor of 1/2, the radius and height of the new cylinder will be half of the original. Let's denote the new radius as (1/2)r and the new height as (1/2)h.
The surface area of the new cylinder is then given by 2π[(1/2)r]² + 2π[(1/2)r][(1/2)h].
Simplifying this expression, we have π(1/4)r² + π(1/4)rh = (1/4)(2πr² + 2πrh) = (1/4)(54π) cm².
Therefore, the surface area of the new cylinder is (1/4)(54π) cm² = 54π/4 cm² = 13.5π cm². Answer: \boxed{13.5\pi}.