One dimension of a cube is increased by 1, another is decreased by 1,

Question

One dimension of a cube is increased by 1, another is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5 less than that of the cube. What was the volume of the cube?

(A) 8
(B) 27
(C) 64
(D) 125
(E) 216

(A) 8
(B) 27
(C) 64
(D) 125
(E) 216

LevanKhukhunashvili · Answer

Let a be the side of the cube. The volume of the cube  a^3 
After adjustment the new figure has the volume: (a-1)(a+1)(a)= a^3 -a

According to the stem:  a^3 -( a^3 -a)=5
a=5

The volume of the initial cube is 125

Imo
Ans:  D

ScottTargetTestPrep · Answer

We can create the equation:

n^3 = (n + 1)(n - 1)n + 5

n^3 = (n^2 - 1)n + 5

n^3 = n^3 - n + 5

n = 5

So the volume of the original cube was 5^3 = 125.

Answer: D

Paras96 · Answer

Let's solve this problem step by step:

Let the original side length of the cube be "x." So, the volume of the cube is V_cube = x^3.

According to the problem:

1. One dimension is increased by 1: (x + 1).
2. Another dimension is decreased by 1: (x - 1).
3. The third dimension is left unchanged: (x).

The volume of the new rectangular solid is 5 less than that of the cube, so we can set up the equation:

V_new = V_cube - 5

Now, we can calculate the volume of the new rectangular solid:

V_new = (x + 1)(x - 1)x

So, we have:

(x + 1)(x - 1)x = x^3 - 5

Now, let's simplify the equation:

(x^2 - 1)x = x^3 - 5

Now, let's distribute and rearrange:

x^3 - x = x^3 - 5

Now, subtract x^3 from both sides:

-x = -5

Now, divide both sides by -1 to solve for x:

x = 5

Now that we've found the value of x, which is the original side length of the cube, we can calculate the volume of the cube:

V_cube = x^3 = 5^3 = 125 cubic units

So, the volume of the cube was 125 cubic units.

Hence D

One dimension of a cube is increased by 1, another is decreased by 1,

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One dimension of a cube is increased by 1, another is decreased by 1,

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