vitorpteixeira wrote:

Is cone P similar to cone Q?

(1) The surface area of P is 9 times the surface area of Q

(2) The volume of P is 9 times the volume of Q

HI..

with 100% answering incorrectly, this may help

thing to remember..

Two cones will be similar when the RADIUS and the HEIGHT are in SAME proportionso \(\frac{R_P}{R_Q}=\frac{H_P}{H_Q}=k\)

let's see the statements

(1) The surface area of P is 9 times the surface area of Q this means \(9*pi*R_P^2+pi*R_P*\sqrt{H_P^2+R_P^2}=pi*R_Q^2+pi*R_Q*\sqrt{H_Q^2+R_Q^2}\)..

so \(9*=pi*R_P^2+pi*R_P*\sqrt{H_P^2+R_P^2}/pi*R_Q^2+pi*R_Q*\sqrt{H_Q^2+R_Q^2}=(R_P^2+R_P*\sqrt{H_P^2+R_P^2})/(R_Q^2+R_Q*\sqrt{H_Q^2+R_Q^2})\)

two cases..

if similar, the ratio \(k = \sqrt{9}=3\)... Possible

or it can be various combination to get the ratio as 9...Possible

Insuff

(2) The volume of P is 9 times the volume of Q\(\frac{1}{3}*pi*R_P^2H_P=9*\frac{1}{3}*pi*R_Q^2H_Q............\frac{R_P^2H_P}{R_Q^2H_Q}=9\)..

two cases

1) if \(k^3=9\) .. similar possible

2) only \(R_P=3*R_Q\)... not similar.. possible

so insuff..

combined..different values of k in both cases so the cones are NOT similar

Sufficient

C

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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