Surface area formulas and volume formulas appear time and again in calculations and homework problems. Pressure is a force per area and density is mass per volume. These are just two simple types of calculations that involve these formulas. This is a short list of common geometric shapes and their surface area formulas and volume formulas.
Sphere Surface Area Formula and Sphere Volume Formula
A sphere is a solid figure where every point on the surface is equidistant from the center of the sphere. This distance is the radius, r, of the sphere.
Surface area = 4πr2
Volume = 4⁄3πr3
Prism Surface Area Formula and Prism Volume Formula
A prism is a geometric shape consisting of a stack of identical base shapes stacked on top of each other to a depth d. This prism is a prism formed by a stack of triangles.
Surface Area of a Prism = 2 × (Area of the base shape) + (Perimeter of base shape) × (d)
Volume of a Prism = (Area of base shape) × d
To find the area and perimeter of the base shape, check out Area Formulas and Perimeter Formulas.
Box Surface Area Formula and Box Volume Formula
A box can be thought of a stack of rectangles L long and W wide piled on top of each other to a depth of D.
Surface Area of a Box = Sum of the areas of each face of the box, or
Surface Area of a Box = 2(L × W) + 2(L × D) + 2(W × D)
Cube Surface Area Formula and Cube Volume Formula
A cube is a special case box where all the sides are the same length.
Surface Area of a Cube = 6a2
Volume of a Cube = a3
Cylinder Surface Area Formula and Cylinder Volume Formula
A cylinder is a prism where the base shape is a circle.
Surface Area of a Cylinder = 2πr2 + 2πrh
Volume of a Cylinder = πr2h
Square Pyramid Surface Area Formula and Pyramid Volume Formula
A pyramid is a solid shape consisting of a polygon base and triangular faces meeting at a common point above the base. A square pyramid is a pyramid where the base polygon is a square.
In the picture above, side a is the same length as side b. All of the face triangles are isosceles triangles meeting at a point h above the base.
For pyramids with identical face triangles (a = b = c)
Surface Area Formula of a Cone and Volume Formula of a Cone
A cone is a pyramid with a circular base with radius r and height h. The side length s can be found using the Pythagorean Theorem.
s2 = r2 + h2
or
s = √( r2 + h2 )
Surface Area of a Cone = πr2 + πrs
Volume of a Cone = 1⁄3( πr2h )