What is the volume of a sphere with diameter 6.4 ft? Use π ≈ 3.14 and round your answer to the nearest whole number.
Understand the Problem
The question asks to calculate the volume of a sphere given its diameter. The diameter is given as 6.4 ft. We need to use the formula for the volume of a sphere, which is V = (4/3) * pi * r^3, where r is the radius of the sphere. Since the diameter is 6.4 ft, the radius is half of that, which is 3.2 ft. We will use 3.14 as approximation for pi.
Answer
137
Answer for screen readers
137
Steps to Solve
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Calculate the radius The radius $r$ is half of the diameter. Given the diameter is 6.4 ft, the radius is: $r = \frac{6.4}{2} = 3.2$ ft
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Apply the volume formula The formula for the volume $V$ of a sphere is: $V = \frac{4}{3} \pi r^3$ Substitute the value of $r = 3.2$ and $\pi \approx 3.14$ into the formula. $V = \frac{4}{3} \times 3.14 \times (3.2)^3$
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Calculate $r^3$ $r^3 = (3.2)^3 = 3.2 \times 3.2 \times 3.2 = 32.768$
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Substitute $r^3$ into the volume formula $V = \frac{4}{3} \times 3.14 \times 32.768$
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Calculate the volume $V = \frac{4 \times 3.14 \times 32.768}{3} = \frac{411.539456}{3} = 137.179818666...$
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Round to the nearest whole number Round the volume to the nearest whole number: $V \approx 137$ cubic feet
137
More Information
The volume of the sphere is approximately 137 cubic feet.
Tips
A common mistake is forgetting to divide the diameter by 2 to find the radius before calculating the volume. Another mistake is not rounding the final answer to the nearest whole number as specified in the problem statement. Finally, using an incorrect formula for the volume of a sphere is another potential mistake.
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