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You work in the packaging department of a company that makes soup. The old soup can is 8 inches high and has a diameter of 4 inches.

Your department is asked to design a bigger soup can that will hold one-and-a-half times as much soup as the old can. Find the height of the bigger soup can if the diameter stays the same.

Respuesta :

semsee45

Answer:

12 inches high

Step-by-step explanation:

  • Volume of a cylinder = [tex]\pi[/tex]r²h
    (where r = radius and h = height)
  • Radius r = 1/2 diameter

First, find the volume of the original can of soup by using the volume of a cylinder formula and r = 2:

Volume of original can of soup = [tex]\pi[/tex] x 2² x 8 = 32[tex]\pi[/tex]

If the new soup can needs to hold 1.5 times as much soup as the original can, multiply the volume of the original can by 1.5:

volume of new can = 32[tex]\pi[/tex] x 1.5 = 48[tex]\pi[/tex]

If the diameter of the new can is the same as the diameter of the original can, then r = 2.

Use the volume of a cylinder formula, set the volume to 48[tex]\pi[/tex] and use r = 2.  Solve for h:

48[tex]\pi[/tex] = [tex]\pi[/tex]2²h

Divide both sides by [tex]\pi[/tex]:  48 = 4h

Divide both sides by 4:  12 = h

Therefore the height of the new can will be 12 in

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