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!