SOLUTION: A cylindrical candle is in a gift box that is a square-based prism. Determine the volume of the empty space in the box.
What is labeled in the book is:
Diameter: 8cm
Hight:16c
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Question 815079: A cylindrical candle is in a gift box that is a square-based prism. Determine the volume of the empty space in the box.
What is labeled in the book is:
Diameter: 8cm
Hight:16cm
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Assuming that the candle fits tightly in the box without wasted space, the diameter of the candle is the width of the box (the length of the side of the square base of the box), and the height of the box is the height of the candle.
A view from the top, with the box open, would look like this:
The volume of the prism the is the box can be calculated as the product
(area of the square base)(height).
The volume of the cylinder that is the candle can be calculated as the product
(area of the circular base)(height).
The length of the square side of the base of the box is , so
area of the square box base = .
The diameter of the candle is twice the radius, so the radius is
, so
area of the circular base = .
Since the height of the candle and of the box is , the difference in volumes is
= about
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