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Math  /  Geometry

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What is the volume of a sphere with a diameter of 3.6 ft , rounded to the nearest tenth of a cubic foot?
Answer Attempt 1 out of 2 □\square ft3\mathrm{ft}^{3} Submit Answer

Studdy Solution

STEP 1

1. The shape in question is a sphere.
2. The diameter of the sphere is 3.6 3.6 feet.
3. The volume needs to be rounded to the nearest tenth of a cubic foot.

STEP 2

1. Recall the formula for the volume of a sphere.
2. Calculate the radius from the diameter.
3. Substitute the radius into the volume formula.
4. Perform the calculation.
5. Round the result to the nearest tenth.

STEP 3

Recall the formula for the volume of a sphere:
V=43πr3 V = \frac{4}{3} \pi r^3

STEP 4

Calculate the radius from the diameter:
r=Diameter2=3.6 ft2=1.8 ft r = \frac{\text{Diameter}}{2} = \frac{3.6 \text{ ft}}{2} = 1.8 \text{ ft}

STEP 5

Substitute the radius into the volume formula:
V=43π(1.8)3 V = \frac{4}{3} \pi (1.8)^3

STEP 6

Perform the calculation:
V=43π(1.8)3 V = \frac{4}{3} \pi (1.8)^3 =43π×5.832 = \frac{4}{3} \pi \times 5.832 ≈24.429 ft3 \approx 24.429 \text{ ft}^3

STEP 7

Round the result to the nearest tenth:
V≈24.4 ft3 V \approx 24.4 \text{ ft}^3
The volume of the sphere is:
24.4 ft3 \boxed{24.4 \text{ ft}^3}

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