Question

Math

Posted 2 months ago

```
Sharon is making a large batch of soup. The soup reaches a height of $25 \mathrm{~cm}$ in a cylindrical pot whose diameter is $30 \mathrm{~cm}$. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are $7 \mathrm{~cm}$ long.
How many whole cubes can Sharon make?
$\square$ whole cubes
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 1

Calculate the volume of the cylindrical pot using the formula for the volume of a cylinder: $V = \pi r^2 h$. Here, the diameter is $30 \, \text{cm}$, so the radius $r = \frac{30}{2} = 15 \, \text{cm}$, and the height $h = 25 \, \text{cm}$

step 2

Substitute the values into the formula: $V = \pi (15)^2 (25) = 5625 \pi \, \text{cm}^3$

step 3

Convert the volume to a numerical value: $5625 \pi \approx 17671.5 \, \text{cm}^3$

step 4

Calculate the volume of one ice cube using the formula for the volume of a cube: $V = a^3$. Here, the edge length $a = 7 \, \text{cm}$

step 5

Substitute the value into the formula: $V = (7)^3 = 343 \, \text{cm}^3$

step 6

Determine the number of whole ice cubes by dividing the volume of the soup by the volume of one ice cube: $\frac{17671.5}{343} \approx 51.5$

step 7

Since only whole cubes can be made, round down to the nearest whole number: $51$

Answer

51 whole cubes

Key Concept

Volume calculation of cylinder and cube

Explanation

To find the number of whole ice cubes that can be made from the soup, calculate the volume of the cylindrical pot and the volume of one ice cube, then divide the total volume of the soup by the volume of one ice cube and round down to the nearest whole number.

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