Distinguishing between surface area and volume

In this lesson, we learn to distinguish between surface area and volume of solid figures. We learn the use of surface area and volume in real world scenarios and their significance.

We first begin by defining surface area and volume of solid figures, their significance and their uses.

Surface area is the sum of the areas of all the faces of the solid figure. Finding surface area of solid figure is like finding how much wrapping paper that is required to cover the solid; it is the area of the outside faces of a box. It is measured in square units.

Volume is the number of unit cubes that make up a solid figure. Volume is the amount of space inside of the solid figure.

What is the volume of a figure that is 5 inches wide, 7 inches tall and 6 inches long?

Solution

Step 1:

Volume of rectangular prism = l × w × h cubic units

Step 2:

Volume of given prism = 5 × 7 × 6

= 210 cubic inches

A cube has height of 6 mm. What is the volume of the cube?

Solution

Step 1:

Volume of cube = a × a × a cubic units

Step 2:

Volume of given cube = 6 × 6 × 6

= 216 cubic mm