Question

Cylinder has a radius of 6 and a height of 15. Cone has a radius of 6 and the height of 15. The sphere has a radius of 6. Which figures have a volume greater than 600 cubic inches? Choose all that apply. Use 3.14 for pi. Show your work. (2 points) Cylinder Cylinder Cone Cone Sphere

Answer 1

To determine which figures have a volume greater than 600 cubic inches, we'll calculate the volume of each figure using the given dimensions and the formula for the volume of each shape.

1. **Volume of the Cylinder**:
The formula for the volume \( V \) of a cylinder is:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
Given \( r = 6 \) and \( h = 15 \):
\[
V = 3.14 \times (6^2) \times 15
\]
\[
V = 3.14 \times 36 \times 15
\]
\[
V = 3.14 \times 540
\]
\[
V = 1695.6 \text{ cubic inches}
\]

2. **Volume of the Cone**:
The formula for the volume \( V \) of a cone is:
\[
V = \frac{1}{3} \pi r^2 h
\]
Given \( r = 6 \) and \( h = 15 \):
\[
V = \frac{1}{3} \times 3.14 \times (6^2) \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 36 \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 540
\]
\[
V = \frac{1}{3} \times 1696.2
\]
\[
V = 565.2 \text{ cubic inches}
\]

3. **Volume of the Sphere**:
The formula for the volume \( V \) of a sphere is:
\[
V = \frac{4}{3} \pi r^3
\]
Given \( r = 6 \):
\[
V = \frac{4}{3} \times 3.14 \times (6^3)
\]
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
\[
V = \frac{4}{3} \times 678.24
\]
\[
V = 902.99 \text{ cubic inches}
\]

### Summary of Volumes:
- **Cylinder**: \( 1695.6 \) cubic inches
- **Cone**: \( 565.2 \) cubic inches
- **Sphere**: \( 904.32 \) cubic inches

### Conclusion:
Figures with a volume greater than 600 cubic inches are:
- **Cylinder (1695.6 cubic inches)**
- **Sphere (904.32 cubic inches)**

The **Cone** does not exceed 600 cubic inches with its volume of \( 565.2 \) cubic inches.

**Final Answer**: Cylinder, Sphere