Volume and Surface Area Formulas

This video tutorial covers the methods for calculating the volume of various geometric solids, including rectangular prisms, cubes, square base pyramids, cylinders, cones, and spheres. Each shape has a specific formula for volume calculation, and the video provides examples and explanations for each. The tutorial emphasizes understanding the dimensions needed for each formula and how to apply them to find the volume accurately.

What is the formula for calculating the volume of a rectangular prism?

• Length + Width + Height

• Length x Width x Height

• 2 x (Length + Width + Height)

• Length x Width

For a cube, how can the volume be expressed if all sides are equal?

• Side x Side

• Side x Side x Side

• Side + Side + Side

• Side x 3

Which of the following is NOT a correct formula for the volume of a square-based pyramid?

• 1/3 x Base Area x Height

• 1/3 x Side^2 x Height

• Base Area x Height

• 1/3 x Base x Height

In a square-based pyramid, where is the height measured from?

• From the center of the base to the apex

• From the apex to the side

• Along the side of the pyramid

• From the base to the side

What is the formula for the volume of a cylinder?

• PI x Diameter x Height

• PI x Radius^2 x Height

• PI x Radius x Height

• 2 x PI x Radius x Height

If a cylinder has a diameter of 10 cm, what is its radius?

• 5 cm

• 10 cm

• 15 cm

• 20 cm

How is the volume of a cone related to the volume of a cylinder with the same base and height?

• It is twice the volume of the cylinder

• It is the same as the volume of the cylinder

• It is one-third the volume of the cylinder

• It is half the volume of the cylinder

What is the formula for calculating the volume of a cone?

• PI x Radius x Height

• 1/3 x PI x Radius^2 x Height

• PI x Radius^2 x Height

• 1/2 x PI x Radius^2 x Height

What is the formula for the volume of a sphere?

• 4/3 x PI x Radius^3

• 3/4 x PI x Radius^3

• 4 x PI x Radius^2

• PI x Radius^3

If the diameter of a sphere is 10 inches, what is the radius?

• 5 inches

• 15 inches

• 2.5 inches

• 10 inches