SOLUTION: write a function rule to represent the situation. the volume V of a cube shaped box whose edge lengths are 1 inch greater than the diameter d of the ball that the box will hold. Va

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Question 1200656: write a function rule to represent the situation. the volume V of a cube shaped box whose edge lengths are 1 inch greater than the diameter d of the ball that the box will hold. Variables: V (volume) d(diameter)

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

Answer: V = (d+1)^3

That expands out to
V = d^3 + 3d^2 + 3d + 1

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Work Shown:

d = diameter of the ball
d+1 = one inch larger than that diameter = side length of the cube

V = volume of the cube
V = (side)*(side)*(side)
V = (side)^3
V = (d+1)^3

Optionally we can expand that out
V = (d+1)^3
V = (d+1)(d+1)^2
V = (d+1)(d^2+2d+1)
V = d(d^2+2d+1)+1(d^2+2d+1)
V = d^3+2d^2+d+d^2+2d+1
V = d^3+(2d^2+d^2)+(d+2d)+1
V = d^3+3d^2+3d+1

The Binomial Theorem is another approach you could take to go from (d+1)^3 to d^3+3d^2+3d+1

Answer by ikleyn(52750)   (Show Source):
You can put this solution on YOUR website!
.

Good question.

See the answer below.

        V = cubic inches.            ANSWER