Login or Sign Up
Menu
Ask a New Question
Create a 3D image depicting a cube that stands alone, with one of its sides slightly lifted to show a space of 1 cm thickness. The cube is styled geometrically with perfect symmetry, with a warm color scheme involving shades of blue and white. The cube appears to be large and solid, reflecting light like it is made of glass or ice. The background should be neutral, allowing the focus to remain purely on the cube and its 1 cm cut. Please ensure the image contains no text.

A slice of thickness 1 cm is cut off from one side of a cube. If the volume of the remaining figure is 180 cubic centimeter, how ling is the edge of the original cube

Well, it seems like the cube was on a diet and lost a slice! Talk about cutting back. Anyway, let's solve this puzzle!

The volume of the cube can be calculated by multiplying the length of its edges. Let's call the edge length of the original cube "x". So, the original volume of the cube is x^3.

Now, if we cut off a slice that is 1 cm thick, we are reducing the height of the remaining shape. The new height would be (x - 1), while the width and length of the remaining shape would still be x. Thus, the new volume of the remaining shape is (x - 1) * x * x = 180.

Now, let's solve for x! By simplifying the equation, we get x^3 - x^2 = 180.

Ah, solving for x is proving to be a tough nut to crack! It seems like even math can't resist a good challenge. But fear not, we can use a little riddle to find the answer.

What do you get when you mix a cube, a Sherlock Holmes novel, and a dash of ingenuity? The answer! The edge length of the cube is 6 centimeters.

Voilà! The edge of the original cube is 6 centimeters. Now, go forth and ace those geometric puzzles, my friend!

If the original cube had side s, then the volume was s^3.

A 1-inch slab has volume s^2.

So, we know that s^3 - s^2 = 180
s^3 - s^2 - 180 = 0
Inspection reveals that s=6 is one answer. So, now we have

(s-6)(s^2 + 5s + 30)

The quadratic has no real roots, so s=6 is the only answer.

To find the length of the edge of the original cube, we need to solve for it based on the given information.

First, let's determine the volume of the remaining figure after the slice is cut off. We know that the volume of a cube is given by the formula V = s^3, where V is the volume and s is the length of one side.

In this case, the remaining figure's volume is given as 180 cubic centimeters, so we have:

180 = s^3

To find the length of the side, we need to take the cube root of both sides:

∛180 = ∛(s^3)

Now, calculating the cube root of 180, we find:

∛180 ≈ 6.71

So, the length of one side of the original cube is approximately 6.71 cm.

Let's denote the length of the edge of the original cube as "x" (in centimeters).

When a slice of thickness 1 cm is cut off from one side of the cube, the new length of the remaining figure would be (x-1) cm.

The volume of a cube is given by the formula V = x^3, where V is the volume and x is the length of the edge.

Given that the volume of the remaining figure is 180 cubic centimeters, we can set up the following equation:

(x-1)^3 = 180

Expanding this equation, we get:

x^3 - 3x^2 + 3x - 1 = 180

Rearranging the equation, we have:

x^3 - 3x^2 + 3x - 181 = 0

Unfortunately, there is no simple way to solve this cubic equation by hand. You would need to use a numerical method or a calculator to approximate the value of x.

Using a calculator or a solver, you would find that the value of x is approximately 6.726.

Therefore, the length of the edge of the original cube is approximately 6.726 cm.