GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
A cylindrical cup is used to fill a bowl, which is in the sh
[#permalink]
26 Oct 2017, 02:23
26 Oct 2017, 02:23
00:00
Question Stats:
66% (02:02) correct
33% (02:50) wrong based on 6 sessions
Hide Show timer Statistics
A cylindrical cup is used to fill a bowl, which is in the shape of a hemisphere (half of a sphere), with milk. If the radius of the cup is half the radius of the hemisphere, and the height of the cup is double its radius, what is the maximum number of cups that can fill the bowl without overflowing it?
A. 2 cups
B. 3 cups
C. 5 cups
D. 6 cups
E. 9 cups
Kudos for correct solution.
A. 2 cups
B. 3 cups
C. 5 cups
D. 6 cups
E. 9 cups
Kudos for correct solution.
Re: A cylindrical cup is used to fill a bowl, which is in the sh
[#permalink]
26 Oct 2017, 04:53
26 Oct 2017, 04:53
1
Let's use letter c for cup and letter e for hemisphere. The information above can be rewritten as \(r_c = \frac{1}{2}r_e\) and \(h_c = 2r_c\).
The volume of the cup, given that it is a cylinder is equal to \(\pi r_c^2 h_c\), while the volume of the hemisphere is half the volume of a sphere, i.e. \(\frac{1}{2}(\frac{4}{3}\pi r_e^3) = \frac{2}{3}\pi r_e^3\). Substituting in the formula for the volume of the cup, using the information given, leads to \(\pi \frac{1}{4}r_e^2 r_e = \frac{1}{4} \pi r_e^3\).
Now we can multiply the volume of the cup by our choices to get the one which does not exceed the volume of the hemisphere.
If we use 2 cups, the volume becomes \(\frac{1}{2} \pi r_e^3\), which is less than \(= \frac{2}{3}\pi r_e^3\).
If we use 3 cups, the volume becomes \(\frac{3}{4} \pi r_e^3\), which is higher than \(= \frac{2}{3}\pi r_e^3\).
Answer A
The volume of the cup, given that it is a cylinder is equal to \(\pi r_c^2 h_c\), while the volume of the hemisphere is half the volume of a sphere, i.e. \(\frac{1}{2}(\frac{4}{3}\pi r_e^3) = \frac{2}{3}\pi r_e^3\). Substituting in the formula for the volume of the cup, using the information given, leads to \(\pi \frac{1}{4}r_e^2 r_e = \frac{1}{4} \pi r_e^3\).
Now we can multiply the volume of the cup by our choices to get the one which does not exceed the volume of the hemisphere.
If we use 2 cups, the volume becomes \(\frac{1}{2} \pi r_e^3\), which is less than \(= \frac{2}{3}\pi r_e^3\).
If we use 3 cups, the volume becomes \(\frac{3}{4} \pi r_e^3\), which is higher than \(= \frac{2}{3}\pi r_e^3\).
Answer A
gmatclubot
Re: A cylindrical cup is used to fill a bowl, which is in the sh [#permalink]
26 Oct 2017, 04:53
Moderators:
