Question

a school is building a sandbox as shown. select all the expressions that represent the volume of the sandbox. a (6×1×2)+(4×5×2) b (10×2)−(4×2×2) c (10×5×2)+(6×7×2) d (10×5×2)+(6×2×2)

Explanation:

Step1: Divide the sandbox into two rectangular - prisms

The sandbox can be divided into two rectangular - prisms. One has dimensions \(6\times5\times2\) and the other has dimensions \(4\times5\times2\) (since \(10 - 6=4\)). The volume of a rectangular prism is \(V = l\times w\times h\). The total volume \(V_{total}=V_1 + V_2=(6\times5\times2)+(4\times5\times2)\).

Step2: Another way is to consider the whole and subtract the missing part

We can consider a larger rectangular prism with dimensions \(10\times5\times2\) and subtract a smaller rectangular prism with dimensions \(4\times2\times2\). So \(V=(10\times5\times2)-(4\times2\times2)\).

Answer:

A. \((6\times5\times2)+(4\times5\times2)\)
B. \((10\times5\times2)-(4\times2\times2)\)