Each edge of one cube is 2 cm longer than each edge of another cube. The volumes of the cubes differ by 98cm^3

Question

Each edge of one cube is 2 cm longer than each edge of another cube. The volumes of the cubes differ by 98cm^3. Find the lengeths of the edges of each cube.

Answer 1

Cube #1 volume = x^3
Cube #2 voume = (x + 2)^3

Difference = 98 = (x + 2)^3 - x^3

Expand and solve for x. good luck!

Answer 2

Volume is equal to Length x Width x Height for a box. Since for a cube, all sides are of equal length, you can also say it's volume is Length x Length x Length ... or (length)^3 [length cubed].

So I'll call the length of one side of the first cube (X) cm. Since the second cube's length is 2 cm longer, than it's length is (2+X) cm.

The difference of their volumes are 98cm^3 so that means:
[volume of cube 2] - [volume of cube 1] = 98cm^3

Your equation will start like this:

(X+2)^3 - (X)^3 = 98
Expand the first term
(X^3) +(6X^2) +(12X) + (8) -(X^3) = 98
Cancel out the (X^3) terms [it's a positive minus a positive]
(6X^2) +(12X) + (8) = 98
Subtract 8 from each side
(6X^2) +(12X) = 90
Factor out 6 from the left side
6[ (X^2) + (12X) ] =90
Divide each side by 6
(X^2) + (12X) = 15
Subtract 15 from each side
(X^2) + (12X) - (15) = 0
Reverse FOIL ... or expand the term on the left ... whatever you call it.
(X-3)(X+5) = 0
I don't know what math you're taking, but that means that one of those terms must be equal to 0. ie: any number multiplied by zero is equal to zero. Therefore
(X-3) = 0 or (X+5) =0
Since those answers are 3 and -5, the only one that makes sense is x=3 (since you're dealing with length, area, and other "real" numbers.

Don't forget to check your answer if X=3

(X+2)^3 - X^3 = 98
(3+2)^3 - 3^3 = 98
(5)^3 - 27 = 98
125 - 27 = 98
98 = 98
Correct!

Answer 3

OK, we have 2 cubes. Let the dimension for the smaller cube be "x". Then the dimension for the larger cube is "x+2" The information given tells us that
(x+2)^3 = x^3 + 98 (the volume of a cube is the product of 3 equal sides)
Expanding the left side, we have:
x^3 + 3(2)x^2 + 3(2)^2 x + 8
Cleaning up 6x^2 + 12x + 8 = 98
Consolidate constants and factor out a 6.
x^2 + 2x = 15
Then x^2+2x-15 = 0
This factors to (x+5)(x-3)=0.
Since we are interested in positive space, we accept x=3, the side of the small square and the side of the large square is 5.

Answer 4

Let x be the edge of one cube and then (x+2) is the edge of the other , the longer one.
"differ"= subtraction
make the equation with volumes
(x+2)^3-x^3=98
x^3+6x^2+12x+8-x^3=98
6x^2 +12x-90=0 with solutions
x1=-5 reject , the edge cannot be negative
x2=3
so x=3 and x+2=3+2=5
the lengths of the edges of each cube are 3 cm and 5cm

Answer 5

The side of the first cube is 3 cm while that of the cube which is longer than the firsr is 5cm.

This value is obtained by equating
x^3 +98 = (x + 2)^3

Answer 6

Here will be your equation:

( x+2)^3 - x^3 = 98

where:
(x+2) is the length of one side of the bigger cube
x is the length of the smaller cube
(x+2)^3 is the volume of the bigger cube
x^3 is the volume of the smaller cube

so solving for x we got x=3 (length of the side of the small cube)
so the length of the side of the bigger cube is x+2 = 3+2 = 5

Answer 7

x^3 +98 = (x+2)^3

x^3 + 98 = x^3 + 3x^2*2 +3x*2^2 +2^3

0= 6x^2 +12x - 90

0 = x^2 +2x - 15

0 = (x+5)(x-3)

x=-5 (degenerate answer) or x=3

thus one cube has lenght 3 and the other has length 5

3^3=27, 5^3=125; 125-27=98

Answer 8

Err is this even possible?