In ceramics class, Robert made a cone with a radius of 2.5 inches and a height of 9 inches. What was the volume of the cone? Use π ≈ 3.14 and round your answer to the nearest whole... In ceramics class, Robert made a cone with a radius of 2.5 inches and a height of 9 inches. What was the volume of the cone? Use π ≈ 3.14 and round your answer to the nearest whole number. Later, Robert made a cylinder with the same radius and height as the cone. What is the volume of the cylinder? Use π ≈ 3.14 and round your answer to the nearest whole number. Complete the sentence below that describes the relationship between the volumes of the cone and cylinder. Use a whole number. The cone and cylinder have the same height and radius, so the volume of the cylinder is _____ times the volume of the cone. Read more

Steps to Solve

1. Calculate the volume of the cone

The formula for the volume of a cone is $V_{cone} = \frac{1}{3} \pi r^2 h$, where $r$ is the radius and $h$ is the height. Given $r = 2.5$ inches and $h = 9$ inches, and $\pi \approx 3.14$, we have: $V_{cone} = \frac{1}{3} \times 3.14 \times (2.5)^2 \times 9$

2. Simplify the equation

$V_{cone} = \frac{1}{3} \times 3.14 \times 6.25 \times 9$ $V_{cone} = 3.14 \times 6.25 \times 3$ $V_{cone} = 3.14 \times 18.75$ $V_{cone} = 58.875$

3. Round the volume of the cone to the nearest whole number

Rounding $58.875$ to the nearest whole number gives $59$.

4. Calculate the volume of the cylinder

The formula for the volume of a cylinder is $V_{cylinder} = \pi r^2 h$, where $r$ is the radius and $h$ is the height. Given $r = 2.5$ inches and $h = 9$ inches, and $\pi \approx 3.14$, we have: $V_{cylinder} = 3.14 \times (2.5)^2 \times 9$

5. Simplify the equation

$V_{cylinder} = 3.14 \times 6.25 \times 9$ $V_{cylinder} = 3.14 \times 56.25$ $V_{cylinder} = 176.625$

6. Round the volume of the cylinder to the nearest whole number

Rounding $176.625$ to the nearest whole number gives $177$.

7. Find the relationship between the volumes of the cone and cylinder

To find how many times the volume of the cone fits into the volume of the cylinder, divide the volume of the cylinder by the volume of the cone: $\frac{V_{cylinder}}{V_{cone}} = \frac{177}{59} = 3$