Surface Area and Volume Formulas for Geometric Shapes

These flashcards summarize important formulas for calculating the surface area and volume of various geometric shapes.

Surface area of a pyramid

S = 1/2lp + B, where l = slant height, p = perimeter of base.

Surface area of a square pyramid

S = sl + s^2, where s = side length of the square.

Volume of a pyramid

V = 1/3BH, where B is the area of the base and H is the height.

Surface area of a cone

S = πrl + πr^2, where r is the radius and l is the slant height.

Volume of a cone

V = 1/3πr^2h, where r is the radius and h is the height.

Surface area of a prism

S = 2B + ph, where B is the area of the base, p is the perimeter of the base, and h is the height.

Volume of a prism

V = Bh, where B is the area of the base and h is the height.

Surface area of a rectangular prism

S = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height.

Volume of a rectangular prism

V = lwh, where l is the length, w is the width, and h is the height.

Surface area of a cube

S = 6s^2, where s is the side length.

Volume of a cube

V = s^3, where s is the side length.

Surface area of a cylinder

S = 2πrh + 2πr^2, where r is the radius and h is the height.

Volume of a cylinder

V = πr^2h, where r is the radius and h is the height.

Surface area of a sphere

S = 4πr^2, where r is the radius.

Volume of a sphere

V = 4/3πr^3, where r is the radius.

Surface area of a hemisphere

S = 3πr^2, where r is the radius.

Volume of a hemisphere

V = 2/3πr^3, where r is the radius.

Area for Base of any Polygon

A = 1/2asn, where a is the length of a side, s is the apothem, and n is the number of sides.

Lateral Area

L = ½ lp (l = slant height, p = product of # of sides and length of sides)

Slant height

r² + h² = l²