Question

raj has a small rectangular garden area as shown in the figure. he wants to expand the garden by doubling the length and width. he will then add 5 inches of soil to the entire area. 36 in 15 in how much soil does raj need to get at the nursery? 2,160 in.³ 2,700 in.³ 5,340 in.³ 10,800 in.³

Explanation:

Step1: Calculate the new length and width

The original length is \(36\) inches. After doubling, the new length \(l = 2\times36=72\) inches.
The original width is \(15\) inches. After doubling, the new width \(w = 2\times15 = 30\) inches.

Step2: Calculate the area of the expanded garden

The area of a rectangle is \(A=l\times w\). Substituting \(l = 72\) and \(w = 30\), we get \(A=72\times30=2160\) square inches.

Step3: Calculate the volume of the soil

The volume of the soil (a rectangular - prism, where the height \(h\) of the soil is \(5\) inches) is \(V=A\times h\). Substituting \(A = 2160\) and \(h = 5\), we get \(V=2160\times5=10800\) cubic inches.

Answer:

\(10,800\space in.^{3}\)