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)
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
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.
Dr M. A ball is not a circle.
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...
To find the ratio of the surface area of the men's basketball to the surface area of the women's basketball, we need to calculate the surface areas of both and then divide them.
The surface area of a basketball can be approximated by the formula:
Surface Area = 4πr^2
where r is the radius of the basketball.
Given that the diameter of the men's basketball is 24.3 centimeters, we can find its radius by dividing the diameter by 2:
Radius of men's basketball = 24.3 cm / 2 = 12.15 cm
Calculating the surface area of the men's basketball:
Surface Area of men's basketball = 4π(12.15 cm)^2
Similarly, for the women's basketball, with a diameter of 23.4 centimeters:
Radius of women's basketball = 23.4 cm / 2 = 11.7 cm
Calculating the surface area of the women's basketball:
Surface Area of women's basketball = 4π(11.7 cm)^2
Now, we can find the ratio by dividing the surface area of the men's basketball by the surface area of the women's basketball:
Ratio = Surface Area of men's basketball / Surface Area of women's basketball
Substituting the values we calculated:
Ratio = (4π(12.15 cm)^2) / (4π(11.7 cm)^2)
Simplifying:
Ratio = (12.15 cm^2) / (11.7 cm^2)
Calculating the result:
Ratio ≈ 1.0393
Rounded to the nearest hundredth, the ratio of the surface area of the men's basketball to the surface area of the women's basketball is approximately 1.04.
So, the correct ratio is not 1854.14 cm² : 1719.34 cm².