Question

what is the volume of the solid figure? explain how you found your answer. 7 in. 20 in. 30 in. 11 in. 4 in. not drawn to scale 3 the solid figure below is made up of two rectangula

Explanation:

Step1: Divide the solid into two rectangular prisms

Let's assume the first prism has dimensions \(l_1 = 30\) in, \(w_1=4\) in, \(h_1 = 11\) in. The second prism has \(l_2=4\) in, \(w_2 = 7\) in, \(h_2=(20 - 11)=9\) in.

Step2: Calculate the volume of the first prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). For the first prism \(V_1=30\times4\times11\).

$$V_1 = 30\times4\times11=1320$$

Step3: Calculate the volume of the second prism

For the second prism \(V_2 = 4\times7\times9\)

$$V_2=4\times7\times9 = 252$$

Step4: Sum the volumes of the two prisms

\(V=V_1 + V_2\)

$$V=1320+252=1572$$

Answer:

The volume of the solid figure is \(1572\) cubic inches.