Question

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

Explanation:

Step1: Analyze the sandbox as two - rectangular prisms

The sandbox can be divided into two rectangular prisms. Let's assume one prism has dimensions length \(l_1\), width \(w_1\), height \(h_1\) and the other has dimensions length \(l_2\), width \(w_2\), height \(h_2\). The volume of a rectangular prism is \(V = l\times w\times h\).

Step2: Identify the dimensions of the two prisms

For the first prism (say \(A\)), assume length \(l_1 = 10\) ft, width \(w_1=2\) ft, height \(h_1 = 2\) ft. For the second prism (say \(B\)), the length \(l_2=(10 - 5)=5\) ft, width \(w_2 = 6\) ft, height \(h_2=2\) ft.

Step3: Calculate the total volume

The total volume \(V\) of the sandbox is the sum of the volumes of the two prisms. \(V=(10\times2\times2)+(5\times6\times2)\).
Let's check each option:

• Option A: \((6\times7\times2)+(4\times5\times2)\) - Incorrect dimensions used.
• Option B: \((2\times10\times2)+(4\times2\times2)\) - Incorrect dimensions used.
• Option C: \((10\times5\times2)+(6\times7\times2)\) - Incorrect dimensions used.
• Option D: \((10\times2\times2)+(6\times2\times2)\) - Correct as per our analysis above.

Answer:

D. \((10\times5\times2)+(6\times2\times2)\)