Question

Volume of cones, cylinders, and spheres practice

Answer 1

Sure! Here are some practice problems involving the volume of cones, cylinders, and spheres, along with the formulas needed to solve them.

### Formulas:
1. **Volume of a Cylinder**: \( V = \pi r^2 h \)
- Where \( r \) is the radius and \( h \) is the height.

2. **Volume of a Cone**: \( V = \frac{1}{3} \pi r^2 h \)
- Where \( r \) is the radius and \( h \) is the height.

3. **Volume of a Sphere**: \( V = \frac{4}{3} \pi r^3 \)
- Where \( r \) is the radius.

### Practice Problems:

1. **Cylinder Problem**:
- A cylinder has a radius of 3 cm and a height of 5 cm. What is the volume of the cylinder?

2. **Cone Problem**:
- A cone has a radius of 4 cm and a height of 9 cm. What is the volume of the cone?

3. **Sphere Problem**:
- A sphere has a radius of 6 cm. What is the volume of the sphere?

4. **Mixed Problem**:
- A cylinder has a radius of 2 m and a height of 10 m. Then, a cone with the same radius (2 m) and a height of 5 m is placed on top of the cylinder. What is the total volume of the cylinder and cone together?

5. **Challenging Problem**:
- A sphere is inscribed in a cylinder of height 10 cm and a radius of 5 cm. What is the volume of the sphere? (Hint: The diameter of the sphere is equal to the height of the cylinder.)

### Solutions:

Once you've attempted to solve the problems, let me know, and I can provide you with the solutions!