A men's basketball is about 24.3 centimeters in diameters , 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 to the nearest tenth.
thank you again
surface area is directly proportional to area, which is direcly proportional to the square of the radius.
ASmens/SAwomen= ( (24.3/2 /23.4/2))^2
= (24.3/23.4)^2=
Put this in your google search window:
(24.3/23.4)^2=
the surface area is proportional to the square of the diameter
M / W = (24.3 / 23.4)^2
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 area of each basketball.
The surface area of a sphere can be calculated using the formula: SA = 4πr^2, where SA is the surface area and r is the radius of the sphere.
Given that the diameter of the men's basketball is 24.3 centimeters, we can calculate the radius by dividing the diameter by 2:
Men's basketball radius = 24.3 cm / 2 = 12.15 cm
Similarly, for the women's basketball, the radius would be:
Women's basketball radius = 23.4 cm / 2 = 11.7 cm
Now, we can calculate the surface area of each basketball using the formula mentioned earlier.
Men's basketball surface area (SA_men) = 4π(12.15 cm)^2
Women's basketball surface area (SA_women) = 4π(11.7 cm)^2
Calculating the surface areas:
SA_men = 4π(147.6225 cm^2)
SA_women = 4π(136.89 cm^2)
Now we can find the ratio of the surface areas by dividing the surface area of the men's basketball by the surface area of the women's basketball:
Ratio = SA_men / SA_women
Ratio = (4π(147.6225 cm^2)) / (4π(136.89 cm^2))
The π cancels out, simplifying the expression to:
Ratio = 147.6225 cm^2 / 136.89 cm^2
Calculating the ratio:
Ratio ≈ 1.0788
Rounding to the nearest tenth, the ratio of the surface area of the men's basketball to the surface area of the women's basketball is approximately 1.1.
Therefore, the ratio is approximately 1.1.