Answer:
Step-by-step explanation:
Width: x
Length: x + 3
Height: x + 3 + 4 = x + 7
Volume of prism = area of cross section x length
Area of cross section = width x height = x ( x + 7 ) = x² + 7x
Volume = (x + 4) x (x² + 7x)
= x³ + 7x² + 4x² + 28x
= x³ + 11x² + 28x
The algebraic expression which shows the volume of the prism is [tex]x^{3}+10x^{2} +21x[/tex].
Volume is basically amount of substance a container can hold in its capacity. Volume of rectangular prism is the product of length, breadth and height of prism.
We know that volume of rectangular prism is L*B*H.
We have been given that width is x cm.
According to question length will be x+3,
Height will be x+3+4
=x+7
Volume will be =x(x+3)(x+7)
Multiply the expressions,
=x([tex]x^{2}[/tex]+3x+7x+21)
=x([tex]x^{2}[/tex]+10x+21)
=[tex]x^{3} +10x^{2} +21x[/tex]
Hence volume of rectangular prism can be expressed as [tex]x^{3} +10x^{2} +21x[/tex].
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