Question

The manufacturer of souvenir baseballs ships each baseball in a cube shaped box with sides lengths of 5x units. The boxes are shipped in a large cube shaped container with sides that measure 10x4 units. How many baseballs will fit in the shipping container? Express the answer in simplified form. I need help please!!! 50 points​

Answer 1

`\Huge \boxed{\boxed{\boxed{\bf{Number\,\ of\,\ baseballs = 8x^9}}}}`

Step-by-step explanation:

To find the number of baseballs that can fit in the container, we need to calculate the volume of both the baseball box and the shipping container. Then, we can divide the volume of the container by the volume of a single baseball box to determine the number of baseballs.

Let's start with the volume of the baseball box. Since it is a cube, all sides have the same length of 5x units. To calculate the volume, we need to multiply the length, width, and height of the cube. In this case, it would be:

`\LARGE \boxed{\tt{Volume\,\ of\,\ baseball box = (5x)(5x)(5x) = 125x^3}}`

Now let's move on to the volume of the shipping container. It is also a cube with sides measuring 10x⁴ units. So, the volume of the container would be:

`\large \boxed{\tt{Volume\,\ of\,\ shipping\,\ container = (10x^4)(10x^4)(10x^4) = 1000x^(12)}}`

To find out how many baseballs can fit in the container, we divide the volume of the container by the volume of a single baseball box:

• 
  `\tt{Number\,\ of\,\ baseballs = (Volume\,\ of\,\ shipping\,\ container )/(Volume\,\ of\,\ baseball\,\ box)}}`

• 
  `\tt{Number\,\ of\,\ baseballs = (1000x^(12) )/(125x^(3) )}`

• 
  `\tt{Number\,\ of\,\ baseballs = 8x^9}`

Therefore, the simplified form of the answer is 8x^9. This means that 8x^9 baseballs can fit in the shipping container.

#BTH1

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Answer 2

8x⁹

Explanation:

To find out how many baseballs will fit in the shipping container, we need to calculate the volume of the box containing one baseball and the volume of the shipping container, and then divide the volume of the shipping container by the volume of one box.

As the boxes and the shipping container are cubes, we can use the formula for the volume of a cube to calculate their volumes.

`\boxed{\begin{array}{l}\underline{\textsf{Volume of a cube}}\\\\V=s^3\\\\\textsf{where $V$ is the volume and $s$ is the side length.}\end{array}}`

Each baseball is shipped in a cube-shaped box with sides measuring 5x units. Therefore, the volume of one box is:

`\begin{aligned}V_{\text{box}} &=(5x)^3 \\&= 5^3 \cdot x^3\\&=125x^3\; \sf cubed\;units\end{aligned}`

The shipping container is also cube-shaped with sides measuring 10x⁴ units. So, the volume of the shipping container is:

`\begin{aligned}V_{\text{container}} &=(10x^4)^3 \\&= 10^3 \cdot (x^4)^3\\&=10^3 \cdot x^(12)\\&=1000x^(12)\; \sf cubed\;units\end{aligned}`

To calculate how many baseballs fit in the container, we can divide the volume of the container by the volume of one box:

`\begin{aligned}\textsf{Number of baseballs} &= \frac{V_{\text{container}}}{V_{\text{box}}} \\\\&= (1000x^(12))/(125x^3)\\\\&=8x^9\; \sf baseballs\end{aligned}`

Therefore, 8x⁹ baseballs will fit in the shipping container.