A cone has a volume of 113.04 cubic meters and a radius of 3 meters. What is its height?
Use and round your answer to the nearest hundredth.

Ask by Lawson Brooks. in the United States

Mar 14,2025

Question

A cone has a volume of 113.04 cubic meters and a radius of 3 meters. What is its height?
Use and round your answer to the nearest hundredth.

Ask by Lawson Brooks. in the United States

Mar 14,2025

UpStudy AI · Accepted Answer

Given the formula for the volume of a cone

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

we substitute the given values $$ V = 113.04 $$ and $$ r = 3 $$:

$$
113.04 = \frac{1}{3} \times 3.14 \times (3)^2 \times h.
$$

Calculate $$(3)^2$$:

$$
(3)^2 = 9.
$$

Thus, the equation becomes

$$
113.04 = \frac{1}{3} \times 3.14 \times 9 \times h.
$$

Multiply $$3.14$$ and $$9$$:

$$
3.14 \times 9 = 28.26.
$$

Then,

$$
113.04 = \frac{1}{3} \times 28.26 \times h.
$$

Compute $$\frac{1}{3} \times 28.26$$:

$$
\frac{28.26}{3} = 9.42.
$$

So the equation simplifies to

$$
113.04 = 9.42 \times h.
$$

Solve for $$ h $$ by dividing both sides by $$9.42$$:

$$
h = \frac{113.04}{9.42}.
$$

Calculating the division gives

$$
h = 12.00.
$$

Thus, the height of the cone is

$$
h \approx 12.00 \text{ meters}.
$$
The height of the cone is approximately 12.00 meters.