# Volume & Surface Area - Arizona State University

Volume & Surface Area Section 6.2 Volume The volume is a measure of the space inside a solid object. Volume is measure of 3 dimensions. The units of volume are cube length or length3. Example of volume units are cm3, cubic

feet, cubic meters or inches3. Surface Area Surface area is the flat area on the surface of a three-dimensional object. What you do is compute the area of all the sides of an object and then add them up. The Cube For an arbitrary cube with edges that have

length L, H, and W. The volume is V = LWH. The surface area of the cube is the sum of the areas of each face. SA = 2LW + 2HW + 2LH. H W L

The Sphere The volume of a sphere with radius r, is V = (4/3)r3. The surface area is SA = 4r2. The cylinder

The volume of the cylinder is height of the cylinder times the area of a circle. V = r2h. The surface area of a cylinder has two parts. The ends are circles so each circle has an area of r2. The lateral surface can be thought of as a rectangle wound into a circle. One side of the rectangle is h, the other side is the circumference of the circle which is 2r. 2r h

h The pyramid and cone The pyramid and cone have similar formulas for their volume. The basic volume formula is V = (1/3)Ah. Where A is the area of the base. For a pyramid, the area of the base A is just the area of a rectangle. For a cone, the area of the base is the area of a circle.

pyramid cone

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