The volume of a cube can be found by multiplying the length times the width times the height of a box (V=lwh or V=s^3). If the volume of a box is 857.375 cubic inches and all of its dimensions are equal, what is the side length of the box in inches. (Round to the nearest hundredth)
Let's assume the side length of the box is x inches.
Since all dimensions are equal, the volume of the box is equal to x * x * x = x^3.
We know that the volume of the box is 857.375 cubic inches, so we can set up the equation x^3 = 857.375.
To solve for x, we need to take the cube root of both sides of the equation.
∛(x^3) = ∛(857.375)
x = ∛(857.375)
Using a calculator, we find that x ≈ 9.26 (rounded to two decimal places).
Therefore, the side length of the box is approximately 9.26 inches.
Rational or Irrational??
Check mark 40
Check mark 81
0.82
0.55555555...
Which one is rational?
1/2
Check mark 5
- . 12546987 . . .
.4451466477...
Rational numbers are numbers that can be expressed as the ratio of two integers.
Let's check the given numbers:
- Check mark 40: Rational. 40 can be expressed as the ratio of 40/1.
- Check mark 81: Rational. 81 can be expressed as the ratio of 81/1.
- 0.82: Rational. It can be expressed as the ratio of 41/50.
- 0.55555555...: Rational. It can be expressed as the ratio of 5/9.
- 1/2: Rational. It is already expressed as the ratio of 1/2.
- Check mark 5: Rational. 5 can be expressed as the ratio of 5/1.
- - . 12546987 . . . : Rational. It can be expressed as the ratio of -139/111.
- .4451466477...: Irrational. It is a non-repeating and non-terminating decimal.
Therefore, the numbers that are rational are:
- Check mark 40
- Check mark 81
- 0.82
- 0.55555555...
- 1/2
- Check mark 5
- - . 12546987 . . .
The number that is irrational is:
- .4451466477...
It's important to note that repeating decimals, like 0.55555555..., can also be expressed as fractions and are considered rational.
To find the side length of the cube, we need to take the cube root of the volume. Let's calculate it step by step:
1. Start with the given volume: V = 857.375 cubic inches.
2. Take the cube root of the volume: ∛857.375 ≈ 9.45.
3. Round the result to the nearest hundredth: 9.45 ≈ 9.45 inches.
Therefore, the side length of the cube is approximately 9.45 inches.
To find the side length of the box, we can use the formula for the volume of a cube, which states that the volume (V) is equal to the side length (s) cubed (V = s^3).
In this case, we are given that the volume of the box is 857.375 cubic inches. We can set up the equation as follows:
857.375 = s^3
To solve for s, we need to take the cube root of both sides of the equation. The cube root of a number can be found using a calculator or the cube root function on most calculators.
Using a calculator, we find that the cube root of 857.375 is approximately 9.4.
Therefore, the side length of the box is approximately 9.4 inches when rounded to the nearest hundredth.