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Question
Math
Posted 2 months ago

Sharon is making a large batch of soup. The soup reaches a height of 25 cm25 \mathrm{~cm} in a cylindrical pot whose diameter is 30 cm30 \mathrm{~cm}. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are 7 cm7 \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=πr2hV = \pi r^2 h. Here, the diameter is 30cm30 \, \text{cm}, so the radius r=302=15cmr = \frac{30}{2} = 15 \, \text{cm}, and the height h=25cmh = 25 \, \text{cm}
step 2
Substitute the values into the formula: V=π(15)2(25)=5625πcm3V = \pi (15)^2 (25) = 5625 \pi \, \text{cm}^3
step 3
Convert the volume to a numerical value: 5625π17671.5cm35625 \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=a3V = a^3. Here, the edge length a=7cma = 7 \, \text{cm}
step 5
Substitute the value into the formula: V=(7)3=343cm3V = (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: 17671.534351.5\frac{17671.5}{343} \approx 51.5
step 7
Since only whole cubes can be made, round down to the nearest whole number: 5151
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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