Answer:
[tex]2x^3+6x^2[/tex]
Step-by-step explanation:
We are given that
Prism's base area =[tex]x^2+3x[/tex]
Formula for finding the volume of a trapezoidal prism =[tex]\frac{1}{2}(b_1+b_2)h[/tex]
Where [tex]\frac{1}{2}(b_1+b_2)[/tex]=Area of base
h=Height of prism
We have to find the expression that can be used to represents the volume of the trapezoidal prism.
Height of prism=2x
Substitute the values in the formula then, we get
Volume of trapezoidal prism=[tex](x^2+3x)\times 2x[/tex]
Volume of trapezoidal prism=[tex]2x^3+6x^2[/tex]
Hence, the expression that can be used to represents the volume of trapezoidal prism is given by
[tex]2x^3+6x^2[/tex]
The volume of the trapezoidal prism is (2x³ + 6x²) cubic units if the the volume of a trapezoidal prism using the formula a = (b1 + b2)h option first is correct.
It is defined as a three-dimensional space enclosed by an object or thing.
The volume of the trapezoidal prism is;
[tex]\rm V = \frac{1}{2} (b_1+b_2)h[/tex]
Where V = The volume of the trapezoidal prism:
And [tex]\rm \frac{1}{2} (b_1+b_2)[/tex] is the base area.
We have prism base area = x² +3x
And height of the prism h = 2x
Now the volume of the prism;
V = (x² +3x)2x
V = (2x³ + 6x²) cubic units
Thus, the volume of the trapezoidal prism is (2x³ + 6x²) cubic units if the the volume of a trapezoidal prism using the formula a = (b1 + b2)h
Learn more about the volume here:
brainly.com/question/16788902
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