Find the volume of the right circular cone with radius 3.5 cm & height 12 cm

Question

Accepted Answer

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

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

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

Given:
- Radius ($ r $) = 3.5 cm
- Height ($ h $) = 12 cm

Substitute these values into the formula:

$$ V = \frac{1}{3} \pi (3.5)^2 (12) $$

First, calculate $ (3.5)^2 $:

$$ (3.5)^2 = 12.25 $$

Now, substitute back into the formula:

$$ V = \frac{1}{3} \pi (12.25) (12) $$

$$ V = \frac{1}{3} \pi (147) $$

$$ V = 49\pi $$

Using the approximation $\pi \approx 3.14$:

$$ V \approx 49 \times 3.14 $$

$$ V \approx 153.86 $$

Rounding to the nearest whole number, the volume is approximately 154 cm³.

Therefore, Option 2 (154 cm³) is the correct answer.

**Explanation for Incorrect Options:**

1. **Option 1 (308 cm³):** This value is too high. The calculation of the volume using the given dimensions does not support this result. The correct calculation yields approximately 154 cm³, not 308 cm³.

2. **Option 3 (77 cm³):** This value is too low. It is roughly half of the correct volume. The calculation clearly shows that the volume is approximately 154 cm³, which is significantly larger than 77 cm³.

3. **Option 4 (231 cm³):** This value is also too high. The correct calculation results in approximately 154 cm³, which is much less than 231 cm³.

In conclusion, the correct volume of the cone, calculated using the given dimensions, is approximately 154 cm³, which corresponds to Option 2.