Question

Find the unknown dimensions and the volume of the composed figure. А A 4 in. 5 in. 5 in. 3 in. 3 in. B 4 in. Enter the correct numbers in the boxes. Hint The dimension of edge A is inches. The dimension of edge B is inches. The volume of the composed figure is cubic inches.

Answer 1

First we will find the dimension of A

A is equal to the sum of the measures in red

$A=5+4+5=14in$

For B

as we can see in the image B=4in

$B=4in$

Then for the volume we will divide the figure in 2 different figures

First we will calculate the volume of the rectangular prims over the line in yellow

$V=l\times w\times h$

where

l=14 in

w=4 in

h=3 in

we substitute the values

$V=14\times4\times3=168in^3$

then we will calculate the volume of the prism under the line, in this case we have

l=4in

w=4in

h=3in

we substitute the values

$V=4\times4\times3=48in^3$

the total volume of the composed figure is

$V=168+48=216in^3$