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A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 21 inches. The scoop is used to transfer molten steel into a cylindrical storage tank with diameter 28 inches. If the scoop is filled to the top, what will be the height of the molten steel in the storage tank?

Write the answer as a decimal, rounded to the nearest tenth.

Sagot :

Semsee45idn

Answer:

31.5 in

Step-by-step explanation:

  • Volume of a hemisphere = (2/3)[tex]\pi[/tex]r³
    (where r is the radius)
  • Volume of a cylinder = [tex]\pi[/tex]r²h
    (where r is the radius and h is the height)
  • radius r = (1/2) diameter

First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:

Volume = (2/3)[tex]\pi[/tex] x 21³ = 6174[tex]\pi[/tex] in³

Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:

                                            [tex]\pi[/tex]14²h = 6174[tex]\pi[/tex]

                                            196[tex]\pi[/tex]h = 6174[tex]\pi[/tex]

 Divide both sides by [tex]\pi[/tex]:        196h = 6174

Divide both sides by 196:          h = 31.5

Therefore, the height of the molten steel in the storage tank is 31.5 in

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