Prism Volume and Surface Area Concepts

The video tutorial covers two examples of calculating the volume and surface area of a pentagonal prism. The first example provides all necessary dimensions, while the second requires finding the apothem using trigonometry. The tutorial explains the formulas for volume and surface area, including lateral and base areas, and demonstrates how to apply them. It also discusses how to find the apothem using tangent ratios and provides a general formula for surface area.

What is the base shape of the prism discussed in the video?

• Triangle

• Hexagon

• Pentagon

• Square

In the first example, what is the length of each side of the pentagon?

• 4 cm

• 6 cm

• 10 cm

• 8 cm

How do you calculate the area of the base of a pentagonal prism?

• Multiply the perimeter by the height

• Use the formula: 5 times half of base times apothem

• Add the lengths of all sides

• Multiply the base by the height

What is the formula for the volume of a prism?

• Base area divided by height

• Base area plus height

• Perimeter times height

• Base area times height

What is the volume of the prism in the first example?

• 492 cm³

• 246 cm³

• 123 cm³

• 369 cm³

How is the lateral surface area of a prism calculated?

• Base area plus perimeter

• Base area times height

• Perimeter times height

• Height divided by perimeter

What is the total surface area of the prism in the first example?

• 246 cm²

• 369 cm²

• 243 cm²

• 123 cm²

In the second example, what is missing that needs to be calculated?

• Volume

• Apothem

• Base length

• Height

How is the apothem of a pentagon calculated using trigonometry?

• Using sine of the angle

• Using tangent of the angle

• Using cosine of the angle

• Using secant of the angle

What is the calculated apothem in the second example?

• 5.5 cm

• 6.0 cm

• 4.1 cm

• 7.2 cm