Surface Area of Pyramids & Cones

Front

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

Back

Surface Area = Base Area + (1/2 * Perimeter of Base * Slant 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

Define 'slant height' in the context of pyramids and cones.

Back

Slant height is the distance from the apex of the pyramid or cone to the midpoint of a side of the base.

Front

What is the base area of a square pyramid with a side length of 4 inches?

Back

Base Area = side² = 4² = 16 square inches.

Front

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

Back

Lateral Surface Area = (1/2 * Perimeter of Base * Slant Height).

Front

If a cone has a radius of 3 inches and a slant height of 5 inches, what is its surface area?

Back

Surface Area = π(3)² + π(3)(5) = 9π + 15π = 24π ≈ 75.4 square inches.

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

What is the surface area of a pyramid with a base area of 20 square meters and a slant height of 6 meters?

Back

Surface Area = Base Area + (1/2 * Perimeter of Base * Slant Height). Calculate perimeter and substitute.

Front

What is the perimeter of a square base with a side length of 5 meters?

Back

Perimeter = 4 * side = 4 * 5 = 20 meters.

Front

How do you find the total surface area of a cone?

Back

Total Surface Area = Base Area + Lateral Surface Area.