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# M70-31

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Math Expert
Joined: 02 Sep 2009
Posts: 58464

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04 Sep 2018, 02:11
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Question Stats:

75% (02:51) correct 25% (03:17) wrong based on 4 sessions

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A cylindrical oil tank is half-full. When placed standing vertically (so that the circular base is on the ground) the oil reaches 3 meters high. When placed horizontally, the oil reaches 2 meters high.

How much oil, in liters, can the tank hold?

A. $$6\pi$$
B. $$12\pi$$
C. $$18\pi$$
D. $$24\pi$$
E. $$48\pi$$

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Math Expert
Joined: 02 Sep 2009
Posts: 58464

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04 Sep 2018, 02:11
Official Solution:

A cylindrical oil tank is half-full. When placed standing vertically (so that the circular base is on the ground) the oil reaches 3 meters high. When placed horizontally, the oil reaches 2 meters high.

How much oil, in liters, can the tank hold?

A. $$6\pi$$
B. $$12\pi$$
C. $$18\pi$$
D. $$24\pi$$
E. $$48\pi$$

We’ll go for PRECISE because all the information we need is in the question.

Cylinder volume can be found using the formula $$\pi r^2h$$. If the oil reaches 3 meters when the cylinder is half-full, the tank’s height is 6. Similarly, the 2 meters the oil reaches when the cylinder is on its side is exactly half the diameter, that is – the radius. Thus, the tank can hold $$\pi *2^2 *6 = 24\pi$$.

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Re M70-31   [#permalink] 04 Sep 2018, 02:11
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# M70-31

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