Volume and Area of Prisms

The video tutorial explains how to calculate the volume of a prism with a regular pentagon base. It covers the steps to find the area of the base using the apothem and perimeter, employing trigonometry to determine the apothem. The tutorial concludes with the final volume calculation by multiplying the base area by the prism's height.

What is the formula to find the volume of a prism?

• Perimeter of the base plus the height

• Area of the base times the height

• Perimeter of the base times the height

• Area of the base plus the height

What shape is the base of the prism in this problem?

• Pentagon

• Triangle

• Square

• Hexagon

How many sides does a regular pentagon have?

• Four

• Five

• Seven

• Six

What is the measure of each central angle in a regular pentagon?

• 60 degrees

• 72 degrees

• 90 degrees

• 108 degrees

What is the first step in finding the area of a regular pentagon?

• Calculate the central angle

• Calculate the apothem

• Calculate the height

• Calculate the perimeter

What trigonometric function is used to find the apothem?

• Cotangent

• Cosine

• Tangent

• Sine

What is the length of the apothem calculated using tangent?

• 5.0

• 7.2

• 2.5

• 3.4409

Why is it important to ensure the calculator is in degree mode?

• To ensure accurate weight calculations

• To ensure accurate angle calculations

• To ensure accurate length calculations

• To ensure accurate volume calculations

What is the formula to find the area of a regular pentagon?

• 1/2 times the apothem times the perimeter

• Apothem squared

• Perimeter squared

• Base times height

What is the perimeter of the pentagon if each side is 5 millimeters?

• 20 millimeters

• 30 millimeters

• 25 millimeters

• 15 millimeters