Question

find the volume of the solid.

Explanation:

Step1: Divide the solid into two rectangular prisms

We can split the given solid into two rectangular - prisms. One prism has dimensions \(3\times3\times7\) and the other has dimensions \(3\times4\times2\).

Step2: Calculate volume of first prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). For the first prism with \(l = 3\), \(w = 3\), and \(h = 7\), we have \(V_1=3\times3\times7 = 63\) \(yd^3\).

Step3: Calculate volume of second prism

For the second prism with \(l = 3\), \(w = 4\), and \(h = 2\), we have \(V_2=3\times4\times2=24\) \(yd^3\).

Step4: Find total volume

The total volume \(V\) of the solid is the sum of the volumes of the two prisms, \(V = V_1+V_2=63 + 24=87\) \(yd^3\).

Answer:

87