SOLUTION: A solid metal sphere rests in a rectangular tray. The radius of the metal ball is 2cm. The width and the length of the base of the tray are 7cm and 12cm respectively. The depth of

Question 1153132: A solid metal sphere rests in a rectangular tray. The radius of the metal ball is 2cm. The width and the length of the base of the tray are 7cm and 12cm respectively. The depth of water in the tray is 2cm.
(a)Find the volume of the water in the tray
(b)If the height of the tray is 55cm, find the volume of water needed to be poured into the tray so that the metal sphere is just submerged.
(correct answer 3 significant figures if necessary)
I have tried to calculate the volume of water with 7*12*2 but still, I failed to get the correct answer which is 152. It would be helpful if you can help me.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

(a) By answering question (a), you should subtract the volume of the half-sphere from the volume of 7*12*2 cubic centimeters. (b) When you complete part (a), the answer to part (b) will be SAME VOLUME added as the answer to the part (a).

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Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
let the volume of the water in the tray be
let the volume of the tray be
let the volume of the sphere be
given:
The radius of the metal ball is .

The depth of water in the tray is
The width and the length of the base of the tray are and respectively. .
The height of the tray is

(a)Find the volume of the water in the tray
will be less then should be because of a ball
since given that the depth of water in the tray is , the length of tray is and the width is
(assuming there is no ball in)
since the depth of water in the tray is and radius of the metal ball is , means half of the metal sphere is in the water
so, we need to deduct volume of the metal sphere from

volume of the ball is:
....., round it to whole number

(b) If the height of the tray is , find the volume of water needed to be poured into the tray so that the metal sphere is just submerged.

the volume the volume of water needed to be poured into the tray so that the metal sphere is just submerged is same as in (a)
-> the volume of water that covers another half of the metal sphere

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