Math Snap

STEP 1

What is this asking?
We need to find the side length of two cubes, one with a volume of $6307 \text{ mm}^3$ and another with a volume of $24411 \text{ ft}^3$, rounded to the nearest tenth.
Watch out!
Don't forget to apply the cube root correctly and keep track of the units!

STEP 2

1. Cube 1 Side Length
2. Cube 2 Side Length

STEP 3

Alright, let's start with the first cube!
We know that the volume of a cube is given by $V = s^3$, where $V$ is the volume and $s$ is the side length.
We're given the volume, so we need to solve for $s$.

STEP 4

To isolate $s$, we'll take the cube root of both sides of the equation.
This gives us $\sqrt[3]{V} = \sqrt[3]{s^3}$.
Since the cube root "undoes" the cubing operation, we get $s = \sqrt[3]{V}$.

STEP 5

Now, let's plug in the given volume of the first cube, which is $V = 6307 \text{ mm}^3$.
So, $s = \sqrt[3]{6307}$.

STEP 6

Using a calculator, we find that $\sqrt[3]{6307} \approx 18.472 \text{ mm}$.

STEP 7

Finally, we need to round to the nearest tenth.
Since the hundredths digit is $7$, which is greater than or equal to $5$, we round up.
So, the side length of the first cube is approximately $18.5 \text{ mm}$.

STEP 8

Now, let's tackle the second cube!
We'll use the same formula: $s = \sqrt[3]{V}$.

STEP 9

This time, the volume is $V = 24411 \text{ ft}^3$.
So, $s = \sqrt[3]{24411}$.

STEP 10

Using a calculator, we find that $\sqrt[3]{24411} \approx 29.012 \text{ ft}$.

STEP 11

Rounding to the nearest tenth, since the hundredths digit is $1$, which is less than $5$, we round down.
So, the side length of the second cube is approximately $29.0 \text{ ft}$.

The side length of the first cube is approximately $18.5 \text{ mm}$.
The side length of the second cube is approximately $29.0 \text{ ft}$.