Calculating Areas and Volumes of Polygons

This video tutorial covers the calculation of volumes for pyramids and cones using various base shapes, including circles, triangles, squares, rectangles, pentagons, and hexagons. Each example demonstrates the application of the volume formula, which involves calculating the area of the base and multiplying it by the height, then dividing by three. The video provides step-by-step instructions and calculations for each shape, ensuring a comprehensive understanding of the process. The tutorial concludes with a preview of the next video, which will continue with additional examples.

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

• One-third of the area of the base times the height

• Area of the base times the height

• Area of the base plus the height

• One-half of the area of the base times the height

If the radius of a circular base is 2 miles and the height is 7 miles, what is the volume of the cone?

• 29.3 miles cubed

• 27.5 miles cubed

• 30 miles cubed

• 28 miles cubed

How do you calculate the area of a right triangle base?

• Base minus height

• Base plus height

• One-half of the base times the height

• Base times height

What is the volume of a pyramid with a triangular base of area 6 miles squared and height 4 miles?

• 10 miles cubed

• 6 miles cubed

• 12 miles cubed

• 8 miles cubed

What is the area of a square base with side length 11 centimeters?

• 121 centimeters squared

• 100 centimeters squared

• 110 centimeters squared

• 144 centimeters squared

How do you calculate the area of a regular polygon base?

• Apothem times the perimeter

• Apothem plus the perimeter

• One-half of the apothem times the perimeter

• One-third of the apothem times the perimeter

What is the volume of a pentagonal pyramid with a base area of 249 yards squared and height 11 yards?

• 930 yards cubed

• 920 yards cubed

• 900 yards cubed

• 913 yards cubed

If a hexagonal pyramid has a base area of 93.6 meters squared and height 9 meters, what is its volume?

• 300 meters cubed

• 290 meters cubed

• 280.8 meters cubed

• 270 meters cubed

What is the side length of a hexagonal base if the apothem is 5.2 meters?

• 6 meters

• 5 meters

• 7 meters

• 8 meters

What is the perimeter of a pentagonal base with side length 12 yards?

• 60 yards

• 50 yards

• 55 yards

• 65 yards