Surface Area of Pyramids and Cones

Front

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

Back

SA = πr² + πrl, where r is the radius and l is the slant height.

Front

Calculate the surface area of a pyramid with a square base of side 9 cm and slant height of 14 cm.

Back

SA = ½(4*9)(14) + 9² = 333 cm².

Front

What does 'slant height' refer to 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

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

Back

SA = π(3)² + π(3)(5) = 28.27 cm².

Front

What is the total surface area of a square-based pyramid with a base area of 100 in² and a lateral area of 500 in²?

Back

SA = Base Area + Lateral Area = 100 in² + 500 in² = 600 in².

Front

Define 'base area' in the context of pyramids and cones.

Back

Base area is the area of the base shape of the pyramid or cone, which can be a triangle, square, or circle.

Front

What is the surface area of a cone with a radius of 4 cm and a height of 3 cm?

Back

First, find the slant height: l = √(r² + h²) = √(4² + 3²) = 5 cm. Then, SA = π(4)² + π(4)(5) = 50.27 cm².

Front

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

Back

Lateral surface area = ½ * perimeter of base * slant height.

Front

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

Back

The slant height is the hypotenuse of a right triangle formed by the height and radius of the cone.