B. Missing Dimensions

Sometimes the area or volume of an object is given as information in a problem and you are asked to find an unknown measurement. Algebra can be used to isolate the unknown.

Example 1

The surface area of a sphere is 128.6 cm2. Determine the diameter of the sphere.

Substitute the value of the surface area into the formula for the surface area of a sphere and solve for r.

Diameter is twice the length of the radius, r.

The diameter of the sphere is 6.4 cm.

Example 2

Determine the height of Jack's head from his chin to the top of his hat, given the volume of his hat is 19.63 in3, the volume of his cylindrical head is 24.54 in3, and the radius if both head and hat is 2.5 inches.

cone (hat)

cylinder (head)

The height of Jack's head, including his hat, is 4.25 inches.