Question: 8. The formula for finding the volume of a cone can be found using $V = \frac{1}{3} Bh$, where $B$ is the area of the base and $h$ is the height of the cone.
a. Solve the equation for $h$. ________
b. Mr. Trill tells his students the value of two variables in the equation are 2,198 cm^3 and 314 cm^2. Explain how you can determine the value of each variable given this information.
1. **State the problem:** We are given the volume formula for a cone: $$V = \frac{1}{3} Bh$$ where $V$ is volume, $B$ is the base area, and $h$ is the height.
2. **Solve the equation for $h$:**
Start with the formula:
$$V = \frac{1}{3} Bh$$
Multiply both sides by 3 to eliminate the fraction:
$$3V = Bh$$
Divide both sides by $B$ to isolate $h$:
$$h = \frac{3V}{B}$$
3. **Explain how to determine the value of each variable given $V = 2198$ cm$^3$ and $B = 314$ cm$^2$:**
- The volume $V$ is given as 2198 cm$^3$.
- The base area $B$ is given as 314 cm$^2$.
Using the formula for $h$:
$$h = \frac{3 \times 2198}{314}$$
Calculate the numerator:
$$3 \times 2198 = 6594$$
Divide:
$$h = \frac{6594}{314}$$
Simplify by canceling common factors:
$$h = \frac{\cancel{6594}}{\cancel{314}} = 21$$ (since $314 \times 21 = 6594$)
4. **Final answer:**
$$h = 21 \text{ cm}$$
**Summary:**
- We rearranged the volume formula to solve for height $h$.
- We substituted the given values for volume and base area.
- We calculated the height to be 21 cm.