FTCE General Knowledge Math Practice Test

What is the correct formula for the total surface area of a rectangular solid?

1. 2LW + 2WH + 2LH

2. LWH

3. 3.14(r^2)(h)/3

4. 4(3.14)(r^3)

The correct answer is: 2LW + 2WH + 2LH

The correct formula for the total surface area of a rectangular solid is indeed 2LW + 2WH + 2LH. This formula accounts for all six faces of the rectangular solid. To break it down: - The term 2LW represents the area of the two length-width rectangles (the top and bottom faces). - The term 2WH accounts for the two width-height rectangles (the front and back faces). - The term 2LH covers the two length-height rectangles (the left and right faces). By summing these areas, you get the total surface area of the solid, which is why this formula is accurate and essential for calculating how much surface is exposed in a three-dimensional rectangular shape. The other formulas provided refer to different geometric shapes: the volume of a rectangular solid is given by LWH, the volume of a cone is given by \( \frac{3.14(r^2)(h)}{3} \), and the volume of a sphere is given by \( 4(3.14)(r^3) \). Each of these has its own specific context and applicability outside of calculating surface area for a rectangular solid.