Find an expression for the volume of a triangular prism where the base of the prism is a right triangle wit...

Question

Find an expression for the volume of a triangular prism where the base of the prism is a right triangle with base 4x + 6 and height x + 5 and the height of the triangular prism is x + 5. Use the expression to find the volume when x = 3. Find an expression for the volume of a triangular prism.
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V(x)=

CramX · Accepted Answer

Step 1: : Recall the formula for the volume of a prism.. A prism is a solid object with two identical faces, called bases, joined by a set of parallelograms. The volume V of a prism is given by the area of the base multiplied by the height of the prism. So, we have Step 2: : Find the area of the right triangle.. Here, the base of the triangle is given by 4x + 6 and the height is x + 5. Plug these values into the formula: Step 3: : Expand the expression for the area.. Step 4: : Factor out the greatest common factor (GCF) from the expression.. Step 5: : Substitute the area A into the volume formula.. Step 6: : Simplify the expression for the volume.. Final Answer: The volume of the triangular prism is given by the expression $V(x) = \frac{1}{2} (x + 5)^2(4x + 6)$ To find the volume when x = 3, substitute x = 3 into the expression: $V(3) = \frac{1}{2} (3 + 5)^2(4 \cdot 3 + 6)$ $V(3) = \frac{1}{2} (8)^2(18)$ $V(3) = 576$ So, the volume of the triangular prism when x = 3 is 576 cubic units.

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Step 1:
: Recall the formula for the volume of a prism.

Step 2:
: Find the area of the right triangle.

Step 3:
: Expand the expression for the area.

Final Answer

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