The volume of a right circular cone is $$ 770 \mathrm{~cm}^{3} $$. If the radius of its base is 7 cm , find its rertical height.

Question

UpStudy AI · Accepted Answer

To find the vertical height $$ h $$ of the right circular cone, we'll use the formula for the volume of a cone:

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

**Given:**
- Volume $$ V = 770 \, \text{cm}^3 $$
- Radius $$ r = 7 \, \text{cm} $$

**Step 1: Plug the known values into the volume formula**

$$
770 = \frac{1}{3} \pi (7)^2 h
$$

$$
770 = \frac{1}{3} \pi \times 49 \times h
$$

$$
770 = \frac{49}{3} \pi h
$$

**Step 2: Solve for $$ h $$**

Multiply both sides by $$ 3 $$ to eliminate the denominator:

$$
770 \times 3 = 49 \pi h
$$

$$
2310 = 49 \pi h
$$

Now, divide both sides by $$ 49 \pi $$:

$$
h = \frac{2310}{49 \pi}
$$

**Step 3: Calculate the numerical value**

$$
h = \frac{2310}{49 \times 3.141592653589793} \approx \frac{2310}{153.93804} \approx 15 \, \text{cm}
$$

**Conclusion:**

The vertical height of the cone is approximately **15 cm**.
The vertical height of the cone is approximately 15 cm.

The volume of a right circular cone is . If the radius of its base is 7 cm , find its rertical
height.