Surface Area and Volume of Cones and Pyramids

The video tutorial covers the concepts of surface area and volume for cones and pyramids, referred to as 'pointy things.' It explains how to calculate the volume as one-third of the base area times the height and details the surface area calculations for cones, including the lateral surface area. The tutorial also includes solving for unknowns in cone equations and provides practical examples and applications of these calculations.

What is the main topic discussed in the video?

• Surface area and volume of cones and pyramids

• Surface area and volume of cylinders

• Surface area and volume of spheres

• Surface area and volume of cubes

How is the volume of a cone or pyramid calculated?

• Base area times height divided by 4

• Base area times height divided by 3

• Base area times height divided by 2

• Base area times height

What is the formula for the lateral surface area of a cone?

• PI R squared plus PI R L

• PI R L

• PI R times R plus L

• PI R squared

What is the volume of a rectangular pyramid with a base area of 27 and height of 8?

• 72 cm³

• 54 cm³

• 90 cm³

• 81 cm³

If a rectangular pyramid has a volume of 260 cubic inches and a base area of 120, what is its height?

• 8.5 inches

• 6.5 inches

• 7.5 inches

• 5.5 inches

What is the exact volume of a cone with a height of 7 cm and a radius of 3 cm?

• 23 PI cm³

• 22 PI cm³

• 24 PI cm³

• 21 PI cm³

Given a cone with a volume of 2009.6 and height of 30, what is the radius?

• 9 inches

• 6 inches

• 7 inches

• 8 inches

What is the exact area of the curved surface of a cone with radius 5 cm and slant height 15 cm?

• 70 PI cm²

• 75 PI cm²

• 80 PI cm²

• 85 PI cm²

If a cone has a surface area of 159 cm² and a radius of 4 cm, what is the slant height?

• 10.7 cm

• 9.7 cm

• 8.7 cm

• 7.7 cm

What is the cost of covering a cone-shaped roof with glass if the surface area is 747.32 square feet and the cost is $40 per square foot?

• $29,892.70

• $29,892.80

• $29,892.90

• $29,892.60