Question

1. the shape of an entertainment center is shown. calculate its volume. explain your work. i first, we decompose this figure. then we solve the volume for each figure. identify composite solid figures around the home with your child. these items could be furniture such as dressers, desks, or cabinets. measure the dimensions and practice finding their volumes by decomposing them. math @ home activity student practice book

Explanation:

Step1: Decompose the figure

The entertainment - center can be decomposed into three rectangular prisms.

Step2: Calculate volume of left prism

The left prism has dimensions \(l = 20\) in, \(w=15\) in, \(h = 25\) in. Using the volume formula \(V=l\times w\times h\), we have \(V_1=20\times15\times25 = 7500\) in³.

Step3: Calculate volume of middle prism

The middle prism has dimensions \(l = 20\) in, \(w = 25\) in, \(h = 25\) in. So \(V_2=20\times25\times25=12500\) in³.

Step4: Calculate volume of right prism

The right prism has dimensions \(l = 20\) in, \(w = 15\) in, \(h = 25\) in. So \(V_3=20\times15\times25 = 7500\) in³.

Step5: Calculate total volume

The total volume \(V = V_1+V_2+V_3=7500 + 12500+7500=27500\) in³.

Answer:

27500 in³