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Mike buys his ice cream packed in a rectangular prism-shaped carton, while Carol buys hers in a cylindrical-shaped carton. The dimensions of the prism are 5 inches by 3.5 inches by 7 inches. The cylinder has a diameter of 5 inches and a height of 7 inches. Which container holds more ice cream? Justify your answer. Determine, to the nearest tenth of a cubic inch, how much more ice cream the larger container holds.

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Volume of Mike's rectangular prism-shaped carton, V_{1} = L x W x H

Where L, W, H are the Length, Width and Height respectively

V_{1} = 5 x 3.5 x 7

= 122.5 cubic inch

Volume of Carol's cylindrical-shaped carton, V_{2} = πr^{2}h

Where r is the radius and h is the height

r = diameter/2

r = 5/2 = 2.5

V_{2} = π(2.5)^{2}(7)

= 137.4cubic inch

Thus, Carol's cylindrical-shaped carton will hold 137.4 - 122.5 more ice cream than Mike's rectangular prism-shaped carton

122.5 - 137.4 = 14.9

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