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 = 4πr ^{2}**

**Volume = ^{4}⁄_{3}πr^{3}**

### 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 = 6a ^{2}**

**Volume of a Cube = a ^{3}**

### 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 = 2πr ^{2} + 2πrh**

**Volume of a Cylinder = πr ^{2}h**

### 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.

**s ^{2} = r^{2} + h**

^{2}or

**s = √( r**

^{2}+ h^{2})**Surface Area of a Cone = πr ^{2} + πrs**

**Volume of a Cone = ^{1}⁄_{3}( πr^{2}h )**