A men's basketball team 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
Do you mean the a men's basketball is 24.3 centimeters in diameter?
yes the person must be talking about the basketball size
(24.3 /23.4)^2
areas of similar objects are in proportion to corresponding length ratio squared
To find the ratio of the surface area of a men's basketball to the surface area of a women's basketball, we need to calculate the surface areas of both spheres.
The formula for the surface area of a sphere is given by A = 4πr², where A is the surface area and r is the radius of the sphere.
First, let's calculate the radius of each basketball by dividing the diameter by 2:
- Men's basketball radius = (24.3 cm) / 2 = 12.15 cm
- Women's basketball radius = (23.4 cm) / 2 = 11.7 cm
Next, plug in the radius values into the surface area formula for the respective basketballs:
- Men's basketball surface area = 4π(12.15 cm)²
- Women's basketball surface area = 4π(11.7 cm)²
Now, let's plug these values into a calculator to get the numerical surface areas.
- Men's basketball surface area ≈ 1854.19 cm² (rounded to two decimal places)
- Women's basketball surface area ≈ 1712.74 cm² (rounded to two decimal places)
Finally, 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 = Men's basketball surface area / Women's basketball surface area
= 1854.19 cm² / 1712.74 cm²
≈ 1.082 (rounded to three decimal places)
Therefore, the ratio of the surface area of a men's basketball to the surface area of a women's basketball is approximately 1.082.