Question

a preschool is building a sandbox. here is a diagram that shows the side lengths of the sandbox. what is the volume of the sandbox? explain or show your reasoning.

Explanation:

Step1: Divide the sandbox into two rectangular - prisms.

The first prism has dimensions \(l = 10\) feet, \(w = 2\) feet, \(h = 5\) feet. The second prism has dimensions \(l=10\) feet, \(w = 6\) feet, \(h = 7\) feet.

Step2: Calculate the volume of the first rectangular - prism.

Use the formula \(V_1=l\times w\times h\). So \(V_1 = 10\times2\times5=100\) cubic feet.

Step3: Calculate the volume of the second rectangular - prism.

Use the formula \(V_2=l\times w\times h\). So \(V_2=10\times6\times7 = 420\) cubic feet.

Step4: Calculate the total volume of the sandbox.

Add the volumes of the two prisms: \(V = V_1+V_2\). So \(V=100 + 420=520\) cubic feet.

Answer:

520 cubic feet