The percent by the volume of the rectangle solid increased 45.2% .
The volume of the rectangular solid is equal to the area of the base times its height. Therefore, the volume of a rectangular solid formula is given as. The volume of a rectangular solid = Length x Width x Height cubic units
According to the question
Let length of triangle = L
Breath of triangle = B
Height of triangle = H
Now ,
Volume of rectangle = Length x Width x Height
= LBH
If the length and width of a rectangular solid are increased by 10% and the height is increased by 20%
Therefore
length of new triangle = 1.1L
Breath of new triangle = 1.1B
Height of new triangle = 1.2H
therefore ,
Volume of new rectangle = Length x Width x Height
= 1.1L*1.1B*1.2H
= 1.452 LBH
Now,
percent by the volume of the rectangle solid increased
= [tex]\frac{ 1.452 LBH - LBH}{LBH} * 100[/tex]
= [tex]\frac{0.452LBH}{LBH} *100[/tex]
= 45.2%
Hence, The percent by the volume of the rectangle solid increased 45.2% .
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