Find the volume (in cm³, rounded to 2 decimal places) of a right circular cone with a diameter of $12 ext{ cm}$ and a height of $5 ext{ cm}$. Use $\pi = \frac{22}{7}$.

Question

Find the volume (in cm³, rounded to 2 decimal places) of a right circular cone with a diameter of $12 	ext{ cm}$ and a height of $5 	ext{ cm}$. Use $\pi = \frac{22}{7}$.

Accepted Answer

**Solution:**

1. Given the diameter of the cone is $12 	ext{ cm}$, so the radius $r = \frac{12}{2} = 6 	ext{ cm}$.

2. The height of the cone is $h = 5 	ext{ cm}$.

3. The formula for the volume of a cone is:
   $$V = \frac{1}{3} \pi r^2 h$$

4. Substitute the values:
   $$V = \frac{1}{3} 	imes \frac{22}{7} 	imes 6^2 	imes 5$$
   $$= \frac{1}{3} 	imes \frac{22}{7} 	imes 36 	imes 5$$

5. Simplify step-by-step:
   $$= \frac{22}{21} 	imes 180 = \frac{22 	imes 180}{21}$$
   $$= \frac{3960}{21} = 188.57 	ext{ cm}^3$$

**Answer:** $188.57 	ext{ cm}^3$

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