Math / Geometry

QuestionThe volume of this cone is $1,519.76$ cubic meters. What is the height of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $h \approx$ $\square$ meters

Studdy Solution

STEP 1

1. The cone has a radius of $11$ meters.
2. The volume of the cone is $1519.76$ cubic meters.
3. Use $\pi \approx 3.14$ .

STEP 2

1. Recall the formula for the volume of a cone.
2. Rearrange the formula to solve for the height.
3. Substitute the given values.
4. Calculate the height.

STEP 3

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

STEP 4

Rearrange the formula to solve for the height $h$ :
$h = \frac{3V}{\pi r^2}$

STEP 5

Substitute the given values into the formula:
$h = \frac{3 \times 1519.76}{3.14 \times 11^2}$

STEP 6

Calculate the height:
$h = \frac{3 \times 1519.76}{3.14 \times 121}$ $h = \frac{4559.28}{379.94}$ $h \approx 12.00$
The height of the cone is approximately:
$\boxed{12.00} \text{ meters}$

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QuestionThe volume of this cone is $1,519.76$ cubic meters. What is the height of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $h \approx$ $\square$ meters

Studdy Solution

STEP 1

1. The cone has a radius of $11$ meters.
2. The volume of the cone is $1519.76$ cubic meters.
3. Use $\pi \approx 3.14$ .

STEP 2

1. Recall the formula for the volume of a cone.
2. Rearrange the formula to solve for the height.
3. Substitute the given values.
4. Calculate the height.

STEP 3

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

STEP 4

Rearrange the formula to solve for the height $h$ :
$h = \frac{3V}{\pi r^2}$

STEP 5

Substitute the given values into the formula:
$h = \frac{3 \times 1519.76}{3.14 \times 11^2}$

STEP 6

Calculate the height:
$h = \frac{3 \times 1519.76}{3.14 \times 121}$ $h = \frac{4559.28}{379.94}$ $h \approx 12.00$
The height of the cone is approximately:
$\boxed{12.00} \text{ meters}$

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QuestionThe volume of this cone is 1,519.761,519.761,519.76 cubic meters. What is the height of this cone? Use π≈3.14\pi \approx 3.14π≈3.14 and round your answer to the nearest hundredth. h≈h \approxh≈ □\square□ meters

Studdy Solution

STEP 1

1. The cone has a radius of 11 11 11 meters.2. The volume of the cone is 1519.76 1519.76 1519.76 cubic meters.3. Use π≈3.14\pi \approx 3.14π≈3.14.

STEP 2

1. Recall the formula for the volume of a cone.2. Rearrange the formula to solve for the height.3. Substitute the given values.4. Calculate the height.

STEP 3

Recall the formula for the volume of a cone:V=13πr2h V = \frac{1}{3} \pi r^2 h V=31​πr2h

STEP 4

Rearrange the formula to solve for the height h h h:h=3Vπr2 h = \frac{3V}{\pi r^2} h=πr23V​

STEP 5

Substitute the given values into the formula:h=3×1519.763.14×112 h = \frac{3 \times 1519.76}{3.14 \times 11^2} h=3.14×1123×1519.76​

STEP 6

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QuestionThe volume of this cone is $1,519.76$ cubic meters. What is the height of this cone? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $h \approx$ $\square$ meters

1. The cone has a radius of $11$ meters.
2. The volume of the cone is $1519.76$ cubic meters.
3. Use $\pi \approx 3.14$ .

1. Recall the formula for the volume of a cone.
2. Rearrange the formula to solve for the height.
3. Substitute the given values.
4. Calculate the height.

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

Rearrange the formula to solve for the height $h$ :
$h = \frac{3V}{\pi r^2}$

Substitute the given values into the formula:
$h = \frac{3 \times 1519.76}{3.14 \times 11^2}$