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Figure shows a rectangular box and a cyl...

Figure shows a rectangular box and a cylinderical market, which has diameter 0.5'' and height 9''. If the box is filled with as many markers as possible, what percentage of the space will be unused ?

A

`21.5%`

B

`24.6%`

C

`29.2%`

D

`31.8%`

Text Solution

Verified by Experts

The correct Answer is:
C
Since the markers are too long to be turned horizontal, they must be gathered together vertically. Put them in rows as long and wide as possible.
Since each marker has diamerter 0.5'', you can fit 12 across and 12 back, for a total of 144 markers. Now all that remains is to find the volume of the markers and the volume of the box.
The volume of the box `=6xx6xx10=360`
The volume of one marker `= pi r^(2)h=pi(0.25)^(2)xx9 ~~1.77`.
The volume of all 144 markers `~~ 144xx 1.77~~ 254.88`
The volume unsed is `360-254.88~~105.12`
The percent unsed is `(105.12)/(360)~~29.2%`, so the answer is (C ).
You're covered the solid geomertry topics that you're likely to encounter on Math 2. You've reviewed the facts and formulas and learned some useful strategies. Now it's time for you to try another set of typical Math 2 solid geometry questions.
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