Pyramid Properties and Volume Calculations

Mr. Han introduces the concept of pyramids, explaining their types and properties. He covers the formulas for calculating the volume and surface area of pyramids, using examples to illustrate these concepts. The video also includes advanced problems and solutions to deepen understanding.

What is the defining characteristic of a right pyramid?

• The base is a regular polygon.

• All faces are triangles.

• The pyramid has a square base.

• The apex is directly above the centroid of the base.

In a regular pyramid, what is true about the lateral faces?

• They are all equilateral triangles.

• They are all isosceles triangles.

• They are all right triangles.

• They are all scalene triangles.

Why is the volume of a pyramid one-third of a prism with the same base and height?

• Because three pyramids can fit into a prism of the same base and height.

• Because a pyramid has fewer faces.

• Because a pyramid is a three-dimensional triangle.

• Because a pyramid is taller than a prism.

How do you calculate the lateral area of a regular pyramid?

• Multiply the base perimeter by the height.

• Multiply half the perimeter of the base by the slant height.

• Multiply the base area by the height.

• Multiply the base area by the slant height.

What is the volume of a pyramid with a base area of 36 square units and a height of 9 units?

• 324 cubic units

• 108 cubic units

• 108 cubic units

• 12 cubic units

If a pyramid has a square base with side length 4 units and a height of 9 units, what is its volume?

• 48 cubic units

• 24 cubic units

• 36 cubic units

• 12 cubic units

What is the side length of a square base if the pyramid's volume is 128 cubic inches and height is 6 inches?

• 10 inches

• 6 inches

• 12 inches

• 8 inches

For a pyramid with a rectangular base of 3 feet by 1.5 feet and a volume of 6 cubic feet, what is the height?

• 2 feet

• 5 feet

• 4 feet

• 3 feet

If two pyramids are similar and the height ratio is 15:10, what is the volume ratio?

• 27:8

• 3:2

• 9:4

• 15:10

What is the width of the base of a triangular pyramid if the volume is 18 cubic centimeters and the height of the pyramid is 9 centimeters?

• 4 centimeters

• 3 centimeters

• 5 centimeters

• 6 centimeters