Question

haleys dad is making a large pot of vegetarian chili and a small pot of beef chili. he is cooking the chili in two cylindrical pots. the large pot has a diameter of 9 inches and is 10 inches tall. the small pot has a diameter of 7 inches and is 6 inches tall. what is the volume of the large pot? round your answer to the nearest whole number. cubic inches what is the difference in the volumes of the large pot and the small pot? round your answer to the nearest whole number. cubic inches

Explanation:

Step1: Calculate the radius of the large pot

The diameter of the large pot is \(d = 9\) inches. The radius \(r=\frac{d}{2}=\frac{9}{2}=4.5\) inches.

Step2: Calculate the volume of the large pot

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Here \(h = 10\) inches and \(r = 4.5\) inches.

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Rounding to the nearest whole number, \(V_{large}\approx636\) cubic inches.

Step3: Calculate the radius of the small pot

The diameter of the small pot is \(d = 7\) inches. The radius \(r=\frac{d}{2}=\frac{7}{2}=3.5\) inches.

Step4: Calculate the volume of the small pot

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Here \(h = 6\) inches and \(r = 3.5\) inches.

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Step5: Calculate the difference in volumes

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Rounding to the nearest whole number, \(\Delta V\approx405\) cubic inches.

Answer:

The volume of the large pot is \(636\) cubic inches.
The difference in the volumes of the large pot and the small pot is \(405\) cubic inches.