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Sagot :
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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