Question

A men's basketball is about 24.3 centimeters in diameter, while the diameter of a women's basketball is about 23.4 centimeters. What is the ratio of the surface area of a men's basketball to the surface area of a women's basketball? Round your answer to the nearest hundredth. Justify your reasoning.

I think the answer is 1854.14 cm squared : 1719.34 cm squared.

PLEASE and Thank you. (My parents said they can't remember)

Answer 1

surface area=4PI*r^2

so the ratio will be the ratios of the radius squared, but since diameters will be in the same ratio, the ratio of mens area to woments area is (24.3/23.4)^2

Answer 2

Surface area of a cirlce is simply its area, or pi(r)^2
Another way to express it is
pi(diameter/2)^2
Remember that diameter is radius times two; radius is therefore diameter divided by two.

Men: pi(24.3/2)^2 = 463.8
Women: pi(23.4/2)^2 = 430.1

Remember, ratio can also be done via division; simply divide your two answers for the ratio.

Answer 3

Dr M. A ball is not a circle.

Answer 4

SA for men's = 4π(12.15)^2
SA for women's = 4π(11.7)^2

ratio of men's to women's
= 4π(12.15)^2 : 4π(11.7)^2
= (12.15)^2 : (11.7)^2
= 147.6225 : 136.89
= 1.078402... : 1
= appr 1.08 : 1

notice that (12.15/11.7)^2= 1.078...