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Leona [35]
3 years ago
13

You are making a sculpture that is a pyramid with a square base. You want the height of the pyramid to be 4 inches less than the

length of a side of the base. You want the volume of the sculpture to be 200 cubic inches. Write a function that gives the volume V of the sculpture in terms of x.
Mathematics
1 answer:
faltersainse [42]3 years ago
8 0

Answer:

The required function that gives the volume V in terms of x is V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}.

Step-by-step explanation:

Consider the provided information.

The height of the pyramid to be 4 inches less than the length of a side of the base.

Let the length of a side of the base is = x

Thus, the height of the pyramid = x-4

The volume of the sculpture is 200 cubic inches

Volume of a pyramid is: V=\dfrac{1}{3} \text{Area of Base}\times\text{Height}

The base of pyramid is square.

So, the area of base = x^2

Substitute the respective values in the above formula.

V=\dfrac{1}{3}\times(x^2)\times(x-4)

V=\dfrac{1}{3}\times(x^3-4x^2)

V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}

Hence, the required function that gives the volume V in terms of x is V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}.

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Step-by-step explanation:

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