SOLUTION: On a glass factory, paperweights are created by pouring molten glass into molds. Each mold is a rectangular prism with a height 5 cm greater than the length of each side of its

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 1185820: On a glass factory, paperweights are created by pouring molten glass into molds. Each mold is a
rectangular prism with a height 5 cm greater than the length of each side of its square base. Each
mold holds 1008 cubic centimeters of glass.
3. If x represents the length of each side of the square base, which of the following mathematical model
satisfy the condition of the above problem?
A. (x + 5) (x) = 1008 B. (x + 5) (x) (x) = 1008
C. (x + 5) (x + 5) (x) = 1008 D. 1008 (x + 5) = (x) (x)
4. What is the height of the glass mold?
5. What are the dimensions of the glass molds? (Follow V = LWH)
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the volume is equal to length * width * height.
length = x
width = x
height = x + 5

the volume is equal to x * x * (x + 5) which is equal to 1008

that's selection B which is (x + 5) * x * x = 1008.

the height of the glass mold is x + 5.

the dimensions of the glass bowl are:
length = x
width = x
height = x + 5

if volume equal length * width * height, then volume = x * x * (x + 5).

selection B says volume is equal to (x + 5) * x * x

that would be height * length * width, or possibly height * width * length.

no matter.

the equations are equivalent.

(x + 5) * x * x give you the same answer as x * x * (x + 5) or x * (x + 5) * x.

i believe that's the commutative law of multiplication.
here's a reference.

https://www.ducksters.com/kidsmath/mathematical_laws.php

you are merely doing height * width * length, or possibly height * length * width.

the base is the part that stands on the ground, i.e. like the base of a lamp.

the length of each side of the square base is x.

that makes the height equal to x + 5.

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

3. The volume 1008 is length * width * height:

ANSWER: B

4.

The equation does not factor. Solve for x using some numerical method like Newton's method, or using a graphing calculator.

ANSWER: to 3 decimal places, the height x+5 is 8.607+5 = 13.607

5.

ANSWERS:
height 13.607
length and width 8.607

CHECK: (8.607)(8.607)(13.607) = 1800 (rounded)