Surface Area and Volume of Pyramids

This video tutorial covers how to calculate the volume and surface area of square-based and triangular pyramids. It explains the formulas for volume and surface area, including the use of slant height for surface area calculations. The tutorial provides practice problems and examples, focusing on both square and equilateral triangle bases.

What is the formula to calculate the volume of a square-based pyramid?

• 1/4 × base area × height

• 1/2 × base area × height

• 1/3 × base area × height

• base area × height

If a square-based pyramid has a base side length of 8 units and a height of 12 units, what is its volume?

• 320 cubic units

• 384 cubic units

• 256 cubic units

• 512 cubic units

What is the slant height of a square-based pyramid used for?

• Measuring the height

• Determining the base area

• Calculating the volume

• Finding the surface area

How do you calculate the lateral area of a square-based pyramid?

• b² + 2bl

• 2bl

• b²

• bl

What is the formula for the volume of a triangular pyramid?

• 1/4 × base area × height

• base area × height

• 1/2 × base area × height

• 1/3 × base area × height

If a triangular pyramid has a base area of 30 square units and a height of 15 units, what is its volume?

• 150 cubic units

• 225 cubic units

• 180 cubic units

• 200 cubic units

What is the formula for the surface area of an equilateral triangular pyramid?

• √3/4 × b² + 3/2 × b × l

• b² + 2bl

• 1/2 × base × height

• b² + 3bl

How many lateral faces does a triangular pyramid have?

• Five

• Three

• Two

• Four

If the slant height of a triangular pyramid is 20 cm and the base side length is 8 cm, what is the lateral area?

• 200 square cm

• 320 square cm

• 160 square cm

• 240 square cm

What is the surface area of a triangular pyramid with a base side length of 8 cm and a slant height of 20 cm?

• 267.7 square cm

• 300 square cm

• 250 square cm

• 280 square cm