Question: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?
(A) 16/9\(\pi\)
(B) 4/\(\pi\)
(C) 12/\(\pi\)
(D) √(2/\(\pi\))
(E) 4√(2/\(\pi\))
“A Container in the Shape of a Right Circular Cylinder is 1/2 Full of Water.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
It is given in the question that a container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, it is asked to find out the diameter of the base of the cylinder, in inches.
Since 36 cubic inches of water occupy 1/2 of the cylinder, then the volume of the cylinder is 72 cubic inches.
The candidate should know the formula of volume of cylinder
So, we have that volume cylinder =\(\pi\) * r2*h = 72
\(\pi\)* \(r^2\)*9 = 72
\(r^2\) = 8/\(\pi\)
r= \(\sqrt{8/{\pi}}\)
r = 2* \(\sqrt{2/{\pi}}\)
Hence the diameter is equal to 2 * r = 2 * 2* \(\sqrt{2/{\pi}}\) = 4 *\(\sqrt{2/{\pi}}\)
Hence E is the correct option.
Approach Solution 2:
The volume of the cylinder is = hr^2(\(\pi\)).
As per the problem statement, if Half of the volume is equal to 36 than the full volume is 72.
Now, since h =9, we will divide 72/9(\(\pi\))
We will get r^2=8/\(\pi\) or r^2=(4*2)/\(\pi\).
Hence, r= 2*Sqrt(2/\(\pi\))
Since 2r = diameter => diameter = 4*Sqrt(2/\(\pi\))
Hence, E is the correct answer.
If the container is 1/2 full of water and the volume of water is 36 when the total volume is twice that, or 72 inches.
Approach Solution 3:
Volume of cylinder = \(\pi\) * r^2 * h
Hence,
72 = \(\pi\) * r^2 * (9)
8 = \(\pi\) * r^2
8/\(\pi\) = r^2
√8 / √\(\pi\) = r
Diameter (d) = 2r
d = 2(√8 / √\(\pi\))
d = 2√8 / √\(\pi\)
d = (2 * √8 * √\(\pi\)) / \(\pi\)
Hence, E is the correct answer.
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