To solve for the height of the cone, we can use the volume formula for a cone:
Response A: \[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Response B: Given:
- \( V = 189 \) ft³,
- \( r = 4 \) ft.
Substituting in the values into the formula: \[ 189 = \frac{1}{3} \pi (4^2) h \] \[ 189 = \frac{1}{3} \pi (16) h \] \[ 189 = \frac{16}{3} \pi h \]
Now, multiplying both sides by 3 to eliminate the fraction: \[ 567 = 16 \pi h \]
Now, substituting \(\pi \approx 3.14\): \[ 567 = 16 (3.14) h \] \[ 567 = 50.24 h \]
Response C: To get \( h \) by itself, divide both sides by 50.24: \[ h \approx \frac{567}{50.24} \] Calculating the right side: \[ h \approx 11.3 \text{ ft} \]
Response D: Height is approximately: \[ h \approx 11.3 \text{ ft} \]
So, the organized answers are: Response A: \( V = \frac{1}{3} \pi r^2 h \)
Response B: \( 189 = \frac{16}{3} \pi h \)
Response C: \( h \approx 11.3 \text{ ft} \)
Response D: Height is approximately 11.3 ft.