During gym class, Edgar's teacher uses sports cones to mark off certain parts of the field outside. A large cone has a height of 9 inches and a radius of 2 inches. What is the volu... During gym class, Edgar's teacher uses sports cones to mark off certain parts of the field outside. A large cone has a height of 9 inches and a radius of 2 inches. What is the volume of a large sports cone? Use π ≈ 3.14 and round your answer to the nearest whole number. A small sports cone has the same radius, but a volume of 30 cubic inches. What is the height of a small sports cone? Use π ≈ 3.14 and round your answer to the nearest whole number. Read more

Steps to Solve

1. Calculate the volume of the large cone

The formula for the volume of a cone is $V = \frac{1}{3} \pi r^2 h$. We are given that the large cone has a height $h = 9$ inches and a radius $r = 2$ inches. We're also told to use $\pi \approx 3.14$. Plugging these values into the formula, we have:

$V = \frac{1}{3} (3.14) (2^2) (9)$

2. Simplify the volume equation

Now, we can simplify the equation:

$V = \frac{1}{3} (3.14) (4) (9)$

$V = (3.14) (4) (3)$

$V = (3.14) (12)$

$V = 37.68$

3. Round the volume to the nearest whole number

Rounding $37.68$ to the nearest whole number, we get $38$.

So, the volume of the large cone is approximately 38 cubic inches.

4. Calculate the height of the small cone

The small cone has the same radius $r = 2$ inches and a volume $V = 30$ cubic inches. We use the same volume formula and solve for $h$:

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

$30 = \frac{1}{3} (3.14) (2^2) h$

5. Isolate the height variable in the equation

Multiply both sides by 3:

$90 = (3.14) (4) h$

$90 = 12.56h$

Divide both sides by 12.56:

$h = \frac{90}{12.56}$

$h \approx 7.165$

6. Round the height to the nearest whole number

Rounding $7.165$ to the nearest whole number, we get $7$.

So, the height of the small cone is approximately 7 inches.