Question

ONE MEDAL!! A dump truck delivers 5 cubic yards of sand for a sand box. How many cubic feet is this?? a. 1 2/3 b. 15 cubic feet c. 45 d.135 cubic feet

Answer 1

\[1 \text{ yard} = 3 \text{ feet}\]Divide both sides by \(1 \text{ yard}\):

\[\frac{1\text{ yard}}{1 \text{ yard}} = \frac{3 \text{ feet}}{1 \text{ yard}}\]\[1 = \frac{3 \text{ feet}}{1 \text{ yard}}\]We can multiply our equation by 1 without changing anything, so we can also multiply it by that fraction. We need to cube the fraction, because we are dealing in cubic yards and feet:

\[5 \text{ yard}^3 = 5\text { yard}^3*(\frac{3 \text{ feet}}{1 \text{ yard}})^3 = 5 \text{ yard}^3 * \frac{3^3 \text{ feet}^3}{1^3 \text{ yard}^3} = 5 \cancel{\text{ yard}^3}*\frac{27 \text{ feet}^3 } {1 \cancel{ \text{ yard}^3} }\]\[=5*27\text{ feet}^3 =\]

Answer 2

Do your conversions like this and make sure the units cancel correctly. If you don't end up with the right units, you did the problem wrong.