Calculating Volumes of Cone, Cylinder, and Sphere

The video tutorial explains how to calculate the volume of three geometric shapes: a cone, a cylinder, and a sphere. It begins by introducing the formulas for each shape's volume, where 'R' represents the radius and 'H' the height. The tutorial then provides step-by-step examples for each shape, demonstrating how to apply the formulas using specific dimensions. The examples include calculating the volume of a cone with a radius of 5 and height of 12, a cylinder with a radius of 8 and height of 7, and a sphere with a radius of 6. The video concludes by summarizing the process of solving for volume in these shapes.

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

• V = πr^2h

• V = πr^3

• V = 1/3πr^2h

• V = 4/3πr^3

What does 'r' represent in the volume formulas?

• Height

• Diameter

• Circumference

• Radius

What does 'h' stand for in the volume formulas?

• Radius

• Height

• Circumference

• Diameter

For a cone with a radius of 5 and height of 12, what is the volume?

• 452.39 cm^3

• 314.16 cm^3

• 150.8 cm^3

• 628.32 cm^3

How do you adjust the formula for a cone's volume compared to a cylinder's?

• Multiply by 1/3

• Multiply by 3

• Divide by 3

• No adjustment needed

Which shape's volume is calculated using the formula V = 1/3πr^2h?

• Cone

• Sphere

• Cube

• Cylinder

What is the volume of a cylinder with a radius of 8 and height of 7 inches?

• 1407.4 in^3

• 1508.6 in^3

• 1609.8 in^3

• 1701.0 in^3

What is the result when calculating the volume of a cylinder with the formula πr^2h?

• The circumference of the base

• The radius of the cylinder

• The area of the base

• The volume of the cylinder

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

• V = 1/3πr^2h

• V = πr^2h

• V = 4/3πr^3

• V = πr^3

If a sphere has a radius of 6, what is its volume?

• 1001.76 ft^3

• 904.78 ft^3

• 1102.22 ft^3

• 800.34 ft^3