Calculating Volumes of 3D Shapes

The video reviews volume calculations for cylinders, spheres, and cones, providing formulas and guidelines. It includes examples for each shape, emphasizing the importance of using correct units and not rounding fractions improperly. The video also covers complex problems involving multiple shapes and real-world applications, encouraging students to practice and reach out for help if needed.

What is the formula to calculate the volume of a cylinder?

• V = 1/3 πr^2h

• V = πr^2h

• V = πr^3

• V = 4/3 πr^3

How do you convert diameter to radius?

• Divide diameter by π

• Multiply diameter by π

• Divide diameter by 2

• Multiply diameter by 2

What is the volume of a cylinder with a radius of 5 units and height of 6 units, using π as 3.14?

• 188.4 units^3

• 94.2 units^3

• 471 units^3

• 282.6 units^3

What is the volume formula for a cone?

• V = 2πr^2h

• V = 4/3 πr^3

• V = 1/3 πr^2h

• V = πr^2h

How is the volume of a cone related to the volume of a cylinder?

• It is double the volume of a cylinder.

• It is the same as the volume of a cylinder.

• It is half the volume of a cylinder.

• It is one-third the volume of a cylinder.

What is the correct formula to calculate the volume of a sphere?

• V = πr^2h

• V = 1/3 πr^2h

• V = 4/3 πr^3

• V = 2/3 πr^3

How do you calculate the volume of a hemisphere?

• Multiply the sphere volume by 1/3

• Multiply the sphere volume by 2

• Use the same formula as for a sphere

• Divide the sphere volume by 2

For a sphere with a diameter of 42 units, what is the radius?

• 21 units

• 84 units

• 14 units

• 42 units

If a spherical ball with a diameter of 12 inches deflates at 4.5 cubic inches per second, how long will it take to fully deflate?

• 50.24 seconds

• 200.96 seconds

• 100.48 seconds

• 401.92 seconds

What is the total volume of four soda cans, each with a height of 3.5 feet and a diameter of 10 inches?

• 1099 cubic inches

• 2198 cubic inches

• 549.5 cubic inches

• 274.75 cubic inches