Question

study the diagram.
4 in 12 ft 20 ft
12 in = 1 ft, 3 ft = 1 yd
a concrete pad is needed to extend a driveway. the dimensions are given on the diagram.
to the nearest cubic yard, how much concrete should be ordered?
a. 3 cubic yd
b. 27 cubic yd
c. 80 cubic yd
d. 230 cubic yd
e. 960 cubic yd

Explanation:

Step1: Convert all dimensions to yards

First, convert the thickness from inches to feet: \( 4 \text{ in} = \frac{4}{12} \text{ ft} = \frac{1}{3} \text{ ft} \). Then convert all dimensions to yards. Since \( 3 \text{ ft} = 1 \text{ yd} \), we have:

• Thickness: \( \frac{1}{3} \text{ ft} = \frac{1}{3} \div 3 = \frac{1}{9} \text{ yd} \)
• Length: \( 12 \text{ ft} = 12 \div 3 = 4 \text{ yd} \)
• Width: \( 20 \text{ ft} = 20 \div 3 = \frac{20}{3} \text{ yd} \)

Step2: Calculate the volume of the concrete pad

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height (thickness here).
Substitute the values:
\( V = 4 \times \frac{20}{3} \times \frac{1}{9} \)
First, calculate \( 4 \times \frac{20}{3} = \frac{80}{3} \)
Then, \( \frac{80}{3} \times \frac{1}{9} = \frac{80}{27} \approx 2.96 \)
Rounding to the nearest cubic yard, we get \( 3 \) cubic yards.

Answer:

A. 3 cubic yd