SOLUTION: Pls Help!!with full explaination : A cylindrical wax candle of radius 5cm and height 28cm, is melted and the wax is poured into a rectangular prism whose cross section is a square

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Question 117582: Pls Help!!with full explaination : A cylindrical wax candle of radius 5cm and height 28cm, is melted and the wax is poured into a rectangular prism whose cross section is a square of side 8 cm. Calculate the height of the wax in the rectangular prism.
(take pi- 22/7)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The candle is modeled as a cylinder of radius, r, and height, h.
The volume of a cylinder is given by the formula,
V%5Bc%5D=%28pi%29r%5E2h
V%5Bc%5D=%2822%2F7%29%285%29%5E2%2828%29
V%5Bc%5D=2200
There is 2200 sq.cm. of wax that gets poured into the prism.
The volume of the rectangular prism is given by
V%5Bp%5D=AL
where A is the cross sectional area.
The cross section of the prism is a square with 8 cm sides.
The area of a square is given by,
A=s%5E2}
A=8%5E2}
A=64
Putting that back into our prism volume equation,
V%5Bp%5D=AL
V%5Bp%5D=64L
We set this equal to the volume of wax and solve for L.
64L=2200
L=34.375
The height of the wax in the prism is 34 3/8 cm.