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08 Dec 2015, 11:46
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C
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Difficulty:
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90% (00:46) correct
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What is the surface area of the cone?
1) Volume = 12pi cm^3
2) The height of the cone is 4 cm
1) Volume = 12pi cm^3
2) The height of the cone is 4 cm
09 Dec 2015, 03:02
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GMATDemiGod
What is the surface area of the cone?
1) Volume = 12pi cm^3
2) The height of the cone is 4 cm
1) Volume = 12pi cm^3
2) The height of the cone is 4 cm
Formulas we should know for cones:
Volume of a cone: \(\frac{1}{3}\)\(\pi\) \(r^{2}\)h
Surface of a cone: \(\pi\)rl, where l is the lateral height, or \(\pi\)r \(\sqrt{r^{2}+h^{2}}\)
1) Volume = 12\(\pi\) \(cm^3\)
\(\frac{1}{3}\)\(\pi\) \(r^{2}\)h = 12\(\pi\) \(cm^3\)
\(r^{2}\)h = 4
we do not know r or h individually, and the combo of \(r^{2}\)h is insufficient for the equation.
Insufficient.
2) The height of the cone is 4 cm
height is useful but we know nothing about the radius of the base of the cone, r.
Insufficient.
(1)+(2) Both statements together
replace h=4 to find \(r^{2}\)
\(r^{2}\)(4) = 4
\(r^{2}\) = 1
we can know find the surface of the cone..
\(\pi\)\(\sqrt{1}\sqrt{1^{2}+4^{2}}\)
looks freaking complicated but we don't really have to solve it, as long as know we have all the variables needed.
my answer: C
09 Dec 2015, 07:27
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
What is the surface area of the cone?
1) Volume = 12pi cm^3
2) The height of the cone is 4 cm
There are 2 variables (radius, height) and 2 equations are given by the conditions, which makes likely that (C) will become our answer.
Looking at the conditions together,
from (pi)(r^2)h=(pi)(r^2)4=12pi, r=root3, which is an unique answer.
The conditions are sufficient and the answer becomes (C).
For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
What is the surface area of the cone?
1) Volume = 12pi cm^3
2) The height of the cone is 4 cm
There are 2 variables (radius, height) and 2 equations are given by the conditions, which makes likely that (C) will become our answer.
Looking at the conditions together,
from (pi)(r^2)h=(pi)(r^2)4=12pi, r=root3, which is an unique answer.
The conditions are sufficient and the answer becomes (C).
For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
