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Math  /  Geometry

QuestionA cone has a volume of 1899.7 cubic meters and a height of 15 meters. What is its radius? Use π≈3.14\pi \approx 3.14 and round your answer to the nearest hundredth. r≈□r \approx \square meters Submit

Studdy Solution

STEP 1

1. The cone has a volume of 1899.7 1899.7 cubic meters.
2. The height of the cone is 15 15 meters.
3. Use π≈3.14\pi \approx 3.14.

STEP 2

1. Recall the formula for the volume of a cone.
2. Rearrange the formula to solve for the radius.
3. Substitute the given values.
4. Calculate the radius and round to the nearest hundredth.

STEP 3

Recall the formula for the volume of a cone:
V=13πr2h V = \frac{1}{3} \pi r^2 h

STEP 4

Rearrange the formula to solve for the radius r r :
r2=3Vπh r^2 = \frac{3V}{\pi h} r=3Vπh r = \sqrt{\frac{3V}{\pi h}}

STEP 5

Substitute the given values into the formula:
r=3×1899.73.14×15 r = \sqrt{\frac{3 \times 1899.7}{3.14 \times 15}}

STEP 6

Calculate the radius:
r=5699.147.1 r = \sqrt{\frac{5699.1}{47.1}} r=120.98 r = \sqrt{120.98} r≈11.00 r \approx 11.00
Round to the nearest hundredth:
r≈11.00 meters r \approx 11.00 \text{ meters}
The radius of the cone is:
r≈11.00 meters r \approx \boxed{11.00} \text{ meters}

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