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Sagot :
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].
What is volume?
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.
How to calculate volume?
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].
Learn more about volume at https://brainly.com/question/463363
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