Volume/Surface Area of Cones and Pyramids

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3) × π × r² × h, where r is the radius and h is the height.

Front

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

Back

Surface Area = πr(r + l), where r is the radius and l is the slant height.

Front

What is the formula for the volume of a pyramid?

Back

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

Front

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

Back

Surface Area = B + (1/2) × P × l, where B is the area of the base, P is the perimeter of the base, and l is the slant height.

Front

What does 'slant height' refer to in cones and pyramids?

Back

Slant height is the distance from the top of the cone or pyramid to the edge of the base along the side.

Front

How do you calculate the area of a circle?

Back

Area = π × r², where r is the radius.

Front

What is the value of π (pi) commonly approximated as?

Back

π is commonly approximated as 3.14.

Front

If the radius of a cone is doubled, how does that affect the volume?

Back

The volume increases by a factor of 4, since volume is proportional to the square of the radius.

Front

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

Back

Volume is directly proportional to the height; if height increases, volume increases.

Front

How do you find the height of a cone if you know the volume and radius?

Back

Rearrange the volume formula: h = (3 × Volume) / (π × r²).