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.

Tags

CCSS.7.G.B.6

Front

What does B represent in the surface area formula?

Back

B represents the base area of the pyramid.

Tags

CCSS.7.G.B.6

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.

Tags

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.7.G.B.6

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.

Tags

CCSS.7.G.B.6

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.

Tags

CCSS.7.G.B.6

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.

Tags

CCSS.3.MD.D.8

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.

Tags

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.HSG.SRT.C.8

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.

Tags

CCSS.7.G.B.6