What Is The Exact Volume Of A Cone With A Height Of 6 And A Radius Of 14?Remember To Use The Formula: $V = \frac{1}{3} \pi R^2 H$A. $60 \pi$ B. $432 \pi$ C. $200 \pi$ D. $392 \pi$

What is the Exact Volume of a Cone with a Height of 6 and a Radius of 14?

Understanding the Formula for the Volume of a Cone

The volume of a cone is a fundamental concept in mathematics, and it is essential to understand the formula that calculates this volume. The formula for the volume of a cone is given by:

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

where $V$ is the volume of the cone, $r$ is the radius of the base of the cone, and $h$ is the height of the cone. This formula is a crucial concept in mathematics, and it is used to calculate the volume of various shapes, including cones.

Calculating the Volume of a Cone with a Height of 6 and a Radius of 14

To calculate the volume of a cone with a height of 6 and a radius of 14, we can use the formula given above. We substitute the values of $r$ and $h$ into the formula and calculate the volume.

$$V = \frac{1}{3} \pi (14)^2 (6)$$

To calculate the value of $V$, we need to follow the order of operations (PEMDAS):

1. Calculate the value of $(14)^2$: $(14)^2 = 196$

2. Substitute the value of $(14)^2$ into the formula:

$$V = \frac{1}{3} \pi (196) (6)$$

3. Calculate the value of $(196) (6)$: $(196) (6) = 1176$

4. Substitute the value of $(196) (6)$ into the formula:

$$V = \frac{1}{3} \pi (1176)$$

5. Calculate the value of $\frac{1}{3} (1176)$: $\frac{1}{3} (1176) = 392$

6. Substitute the value of $\frac{1}{3} (1176)$ into the formula:

$$V = 392 \pi$$

Conclusion

The exact volume of a cone with a height of 6 and a radius of 14 is $392 \pi$. This is calculated using the formula for the volume of a cone, which is given by:

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

We substitute the values of $r$ and $h$ into the formula and calculate the volume, following the order of operations (PEMDAS).

Answer

The correct answer is:

• D. $392 \pi$

Explanation

The correct answer is $392 \pi$ because we calculated the volume of the cone using the formula:

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

We substituted the values of $r$ and $h$ into the formula and calculated the volume, following the order of operations (PEMDAS). The final answer is $392 \pi$.
What is the Exact Volume of a Cone with a Height of 6 and a Radius of 14? - Q&A

Understanding the Formula for the Volume of a Cone

The volume of a cone is a fundamental concept in mathematics, and it is essential to understand the formula that calculates this volume. The formula for the volume of a cone is given by:

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

where $V$ is the volume of the cone, $r$ is the radius of the base of the cone, and $h$ is the height of the cone. This formula is a crucial concept in mathematics, and it is used to calculate the volume of various shapes, including cones.

Calculating the Volume of a Cone with a Height of 6 and a Radius of 14

To calculate the volume of a cone with a height of 6 and a radius of 14, we can use the formula given above. We substitute the values of $r$ and $h$ into the formula and calculate the volume.

$$V = \frac{1}{3} \pi (14)^2 (6)$$

To calculate the value of $V$, we need to follow the order of operations (PEMDAS):

1. Calculate the value of $(14)^2$: $(14)^2 = 196$

2. Substitute the value of $(14)^2$ into the formula:

$$V = \frac{1}{3} \pi (196) (6)$$

3. Calculate the value of $(196) (6)$: $(196) (6) = 1176$

4. Substitute the value of $(196) (6)$ into the formula:

$$V = \frac{1}{3} \pi (1176)$$

5. Calculate the value of $\frac{1}{3} (1176)$: $\frac{1}{3} (1176) = 392$

6. Substitute the value of $\frac{1}{3} (1176)$ into the formula:

$$V = 392 \pi$$

Q&A

Q: What is the formula for the volume of a cone?

A: The formula for the volume of a cone is given by:

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

Q: How do I calculate the volume of a cone with a height of 6 and a radius of 14?

A: To calculate the volume of a cone with a height of 6 and a radius of 14, we can use the formula given above. We substitute the values of $r$ and $h$ into the formula and calculate the volume.

Q: What is the order of operations (PEMDAS) that I need to follow to calculate the volume of a cone?

A: To calculate the volume of a cone, we need to follow the order of operations (PEMDAS):

1. Calculate the value of $(r)^2$
2. Substitute the value of $(r)^2$ into the formula
3. Calculate the value of $(r)^2 (h)$
4. Substitute the value of $(r)^2 (h)$ into the formula
5. Calculate the value of $\frac{1}{3} (r)^2 (h)$
6. Substitute the value of $\frac{1}{3} (r)^2 (h)$ into the formula

Q: What is the final answer for the volume of a cone with a height of 6 and a radius of 14?

A: The final answer for the volume of a cone with a height of 6 and a radius of 14 is $392 \pi$.

Conclusion

The exact volume of a cone with a height of 6 and a radius of 14 is $392 \pi$. This is calculated using the formula for the volume of a cone, which is given by:

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

We substitute the values of $r$ and $h$ into the formula and calculate the volume, following the order of operations (PEMDAS).

Answer

The correct answer is:

• D. $392 \pi$

Explanation

The correct answer is $392 \pi$ because we calculated the volume of the cone using the formula:

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

We substituted the values of $r$ and $h$ into the formula and calculated the volume, following the order of operations (PEMDAS). The final answer is $392 \pi$.