A soccer ball has a volume of 10770.86 cubic centimeters. What is the diameter of this soccer ball? Round your answer to the nearest tenth. Use the approximate value of π, which is 3.14.Answer:Question 4
Question
A soccer ball has a volume of 10770.86 cubic centimeters. What is the diameter of this soccer ball? Round your answer to the nearest tenth. Use the approximate value of π, which is 3.14.Answer:Question 4
Solution
To find the diameter of the soccer ball, we first need to understand that the volume of a sphere (which a soccer ball is) can be calculated using the formula:
V = 4/3 * π * r³
Where V is the volume, r is the radius, and π is a mathematical constant whose approximate value is 3.14.
Given that the volume of the soccer ball is 10770.86 cubic centimeters, we can rearrange the formula to solve for the radius:
r = ∛(3V / 4π)
Substituting the given values:
r = ∛(3 * 10770.86 / 4 * 3.14) r = ∛(32312.58 / 12.56) r = ∛(2571.5) r = 13.7 cm
The diameter of a sphere is twice the radius, so:
d = 2r d = 2 * 13.7 d = 27.4 cm
So, the diameter of the soccer ball is approximately 27.4 cm, rounded to the nearest tenth.
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