Find the volume of a right circular cone that has a height of 13.8 ft and a
base with a radius of 7.8 ft . Round your answer to the nearest tenth of a
cubic foot.
Answer Attempt 1 out of 2

Question

Find the volume of a right circular cone that has a height of 13.8 ft and a base with a radius of 7.8 ft . Round your answer to the nearest tenth of a cubic foot. Answer Attempt 1 out of 2

UpStudy AI · Accepted Answer

To find the volume of a right circular cone, we can use the formula:

$$ V = \frac{1}{3} \pi r^2 h $$

where:
- $$ V $$ is the volume of the cone,
- $$ r $$ is the radius of the base of the cone,
- $$ h $$ is the height of the cone.

Given:
- Height of the cone, $$ h = 13.8 $$ ft,
- Radius of the base of the cone, $$ r = 7.8 $$ ft.

Substitute the given values into the formula:

$$ V = \frac{1}{3} \pi (7.8)^2 (13.8) $$

Now, we can calculate the volume of the cone.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{3}\pi \times 7.8^{2}\times 13.8$$
- step1: Convert the expressions:
  $$\frac{1}{3}\pi \left(\frac{39}{5}\right)^{2}\times 13.8$$
- step2: Multiply the terms:
  $$\frac{23}{5}\pi \left(\frac{39}{5}\right)^{2}$$
- step3: Multiply:
  $$\frac{23\pi }{5}\left(\frac{39}{5}\right)^{2}$$
- step4: Evaluate the power:
  $$\frac{23\pi }{5}\times \frac{39^{2}}{5^{2}}$$
- step5: Multiply the fractions:
  $$\frac{23\pi \times 39^{2}}{5\times 5^{2}}$$
- step6: Multiply:
  $$\frac{34983\pi }{5^{3}}$$
- step7: Evaluate the power:
  $$\frac{34983\pi }{125}$$
The volume of the right circular cone is approximately 879.218686 cubic feet.

Rounding to the nearest tenth of a cubic foot, the volume of the cone is approximately 879.2 cubic feet.
The volume of the cone is approximately 879.2 cubic feet.

Find the volume of a right circular cone that has a height of 13.8 ft and a
base with a radius of 7.8 ft . Round your answer to the nearest tenth of a
cubic foot.
Answer Attempt 1 out of 2

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