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Math  /  Geometry

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A cylinder has a base diameter of 6 meters and a height of 14 meters. What is its volume in cubic meters, to the nearest tenths place?

Studdy Solution

STEP 1

1. The cylinder has a circular base.
2. The diameter of the base is 6 6 meters.
3. The height of the cylinder is 14 14 meters.
4. Use π≈3.14159\pi \approx 3.14159 for calculations.

STEP 2

1. Calculate the radius of the base.
2. Recall the formula for the volume of a cylinder.
3. Substitute the given values.
4. Calculate the volume.
5. Round the result to the nearest tenths place.

STEP 3

Calculate the radius of the base:
The radius r r is half of the diameter: r=Diameter2=6 m2=3 m r = \frac{\text{Diameter}}{2} = \frac{6 \text{ m}}{2} = 3 \text{ m}

STEP 4

Recall the formula for the volume of a cylinder:
V=πr2h V = \pi r^2 h

STEP 5

Substitute the given values into the formula:
V=π(3 m)2(14 m) V = \pi (3 \text{ m})^2 (14 \text{ m})

STEP 6

Calculate the volume:
V=π×9 m2×14 m V = \pi \times 9 \text{ m}^2 \times 14 \text{ m} V=π×126 m3 V = \pi \times 126 \text{ m}^3 V≈3.14159×126 m3 V \approx 3.14159 \times 126 \text{ m}^3 V≈395.84034 m3 V \approx 395.84034 \text{ m}^3

STEP 7

Round the result to the nearest tenths place:
V≈395.8 m3 V \approx 395.8 \text{ m}^3
The volume of the cylinder is:
395.8 m3 \boxed{395.8 \text{ m}^3}

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