SOLUTION: The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube. The length of the box is 2 ft more than the length of an edge of the cube its width is equal to the
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Question 531784: The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube. The length of the box is 2 ft more than the length of an edge of the cube its width is equal to the length of an edge of the cube; and its height is 1 ft more than the length of an edge of the cube. What are the dimensions of the box and the cube? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube. The length of the box is 2 ft more than the length of an edge of the cube its width is equal to the length of an edge of the cube; and its height is 1 ft more than the length of an edge of the cube. What are the dimensions of the box and the cube?
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let x = the side of the cube
Write an equation for each statement:
"The volume of a rectangular box is 6 ft^3 more than twice the volume of a cube."
L * W * H = 2x^3 + 6
:
" The length of the box is 2 ft more than the length of an edge of the cube"
L = x + 2
:
"its width is equal to the length of an edge of the cube;"
W = x
:
"its height is 1 ft more than the length of an edge of the cube."
H = x + 1
:
Substituting for L,W,H
(x+2)*x*(x+1) = 2x^3 + 6
x(x^2 + x + 2x + 2) = 2x^3 + 6
x(x^2 + 3x + 2) = 2x^3 + 6
x^3 + 3x^2 + 2x = 2x^3 + 6
Combine like terms on the left
x^3 - 2x^3 + 3x^2 + 2x - 6 = 0
-x^3 + 3x^2 + 2x - 6 = 0
:
Graph this equation, there are two positive solutions but x=3 is an integer
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What are the dimensions of the box and the cube?
x = 3 inches the side of the cube
then
L = 3+2 = 5 inches
W = 3 inches
H = 3+1 = 4 inches
:
:
Check this
5*3*4 = 2(3^3) + 6
60 = 2(27) + 6
