Find the volume of a right circular cone that has a height of 6.5 cm and a
base with a radius of 8.5 cm . Round your answer to the nearest tenth of a
cubic centimeter.
Answer Attempt 1 out of 2

Question

Find the volume of a right circular cone that has a height of 6.5 cm and a base with a radius of 8.5 cm . Round your answer to the nearest tenth of a cubic centimeter. 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, $$ h = 6.5 $$ cm,
- Radius of the base of the cone, $$ r = 8.5 $$ cm.

Substitute the given values into the formula:

$$ V = \frac{1}{3} \pi (8.5)^2 (6.5) $$

Now, we can calculate the volume of the cone.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{3}\pi \times 8.5^{2}\times 6.5$$
- step1: Convert the expressions:
  $$\frac{1}{3}\pi \left(\frac{17}{2}\right)^{2}\times 6.5$$
- step2: Multiply the terms:
  $$\frac{13}{6}\pi \left(\frac{17}{2}\right)^{2}$$
- step3: Multiply:
  $$\frac{13\pi }{6}\left(\frac{17}{2}\right)^{2}$$
- step4: Evaluate the power:
  $$\frac{13\pi }{6}\times \frac{17^{2}}{2^{2}}$$
- step5: Multiply the fractions:
  $$\frac{13\pi \times 17^{2}}{6\times 2^{2}}$$
- step6: Multiply:
  $$\frac{3757\pi }{24}$$
The volume of the right circular cone is approximately 491.79015 cubic centimeters.

Rounded to the nearest tenth of a cubic centimeter, the volume of the cone is approximately 491.8 cubic centimeters.
The volume of the cone is approximately 491.8 cubic centimeters.

Find the volume of a right circular cone that has a height of 6.5 cm and a
base with a radius of 8.5 cm . Round your answer to the nearest tenth of a
cubic centimeter.
Answer Attempt 1 out of 2

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