Volume and Surface Area of Square-based Pyramids

Front

What is the formula for the surface area of a square-based pyramid?

Back

SA = ½lp + B, where l is the slant height, p is the perimeter of the base, and B is the area of the base.

Front

What does B represent in the surface area formula?

Back

B represents the base area of the pyramid.

Front

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

Back

Volume (V) = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

Front

If the base of a square pyramid has a side length of 4m, what is the area of the base?

Back

The area of the base (B) = side × side = 4m × 4m = 16m².

Front

What is the slant height of a pyramid?

Back

The slant height is the distance from the top of the pyramid to the midpoint of one of the sides of the base.

Front

Calculate the surface area of a square pyramid with a base area of 16m² and a slant height of 5m.

Back

SA = ½(4 × 4) × 5 + 16 = 10 + 16 = 26m².

Front

What is the perimeter of the base of a square pyramid with a side length of 3m?

Back

Perimeter (p) = 4 × side = 4 × 3m = 12m.

Front

If a square pyramid has a height of 6m and a base area of 25m², what is its volume?

Back

V = (1/3)Bh = (1/3)(25m²)(6m) = 50m³.

Front

What is the relationship between the height and slant height of a pyramid?

Back

The slant height is the hypotenuse of a right triangle formed by the height, half the base length, and the slant height.

Front

Find the surface area of a square pyramid with a base side of 5m and a slant height of 7m.

Back

SA = ½(4 × 5) × 7 + 25 = 70 + 25 = 95m².