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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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Answer:

The Cylindrical-shaped container hold more ice-cream and it is 24.9 [tex]in^{3}[/tex]

Step-by-step explanation:

Given:

  • Mike buys his ice cream packed in a rectangular prism-shaped carton (5 inches by 3.5 inches by 7 inches)
  • Carol buys hers in a cylindrical-shaped carton(diameter of 5 inches<=> radius is: 2.5 inches and a height of 7 inches)

=> the volume of the:

Rectangular prism carton is: 5*7*3.5 = 112.5 [tex]in^{3}[/tex]

Cylindrical-shaped carton is: 7*π*[tex]2.5^{2}[/tex] = 137.4  [tex]in^{3}[/tex]

So the Cylindrical-shaped container hold more ice-cream and it is:  137.4 - 112.5 = 24.9 [tex]in^{3}[/tex]

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