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Find the volume of a rectangular prism if the length is \(4x\), the width is \(2x\), and the height is \(x^3 + 3x + 6\).

Use the formula \(V = l \cdot w \cdot h\), where \(l\) is length, \(w\) is width, and \(h\) is height, to find the volume.

A. \(6x^5 + 18x^3 + 36x^2\)

B. \(6x^6 + 18x^3 + 36x^2\)

C. \(8x^5 + 24x^3 + 48x^2\)

D. \(8x^6 + 24x^3 + 48x^2\)

Answer :

Final answer:

The volume of the rectangular prism with length 4x, width 2x, and height x³ + 3x + 6 is 8x⁵ + 24x³ + 48x².

Explanation:

To find the volume of the rectangular prism, you'll need to use the formula V=lwh. Given the length is 4x, width is 2x and height is x³ + 3x + 6, substitute these values into the formula: V = 4x * 2x * (x³ + 3x + 6). This simplifies to V = 8x² * (x³ + 3x + 6) = 8x⁵ + 24x³ + 48x². So the volume of the rectangular prism using the given dimensions is 8x⁵ + 24x³ + 48x².

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Final answer:

By plugging the given dimensions into the volume formula for a rectangular prism and simplifying, the volume of the prism is found to be 8x⁵ + 24x³ + 48x².

Explanation:

The formula for finding the volume of a rectangular prism is V = l * w * h, where l is the length, w is the width, and h is the height. In this case, the length, width, and height are given as 4x, 2x, and x³ + 3x + 6 respectively.

To solve this, we simply substitute these values into the formula: V = (4x) * (2x) * (x³ + 3x + 6). Multiply the terms together to find the volume:

V = 8x² *(x³ + 3x + 6)= 8x⁵ + 24x³ + 48x². Therefore, the volume of the rectangular prism (represented by the polynomial) is 8x⁵ + 24x³ + 48x².

So, the correct answer is (d) 8x⁵ + 24x³ + 48x²

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