Surface Area and Volume of Pyramids and Cones

Front

What is the formula for the surface area of a pyramid?

Back

Surface Area = Base Area + Lateral Area

Front

What is the formula for the volume of a pyramid?

Back

Volume = (1/3) × Base Area × Height

Front

What is the formula for the surface area of a cone?

Back

Surface Area = πr² + πrl (where r is the radius and l is the slant height)

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3) × πr²h (where r is the radius and h is the height)

Front

Define lateral area in the context of pyramids and cones.

Back

Lateral area is the area of the sides of the pyramid or cone, excluding the base.

Front

How do you calculate the base area of a square pyramid?

Back

Base Area = side² (where side is the length of one side of the square base).

Front

What is the slant height of a pyramid?

Back

The slant height is the distance from the top vertex of the pyramid to the midpoint of a side of the base.

Front

If a cone has a radius of 3 cm and a height of 4 cm, what is its volume?

Back

Volume = (1/3) × π(3)²(4) = 12π ≈ 37.68 cm³.

Front

What is the relationship between the height and slant height of a right cone?

Back

The slant height can be found using the Pythagorean theorem: l = √(r² + h²), where r is the radius and h is the height.

Front

Calculate the surface area of a cone with a radius of 5 cm and a slant height of 13 cm.

Back

Surface Area = π(5)² + π(5)(13) = 25π + 65π = 90π ≈ 282.74 cm².