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Intern  Joined: 26 Jul 2015
Posts: 18
Location: Chile
GMAT 1: 620 Q38 V37 GMAT 2: 690 Q49 V35 WE: Analyst (Consulting)
The formula for the surface of a sphere is S=4πr^2. Two lead balls  [#permalink]

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3 00:00

Difficulty:   5% (low)

Question Stats: 86% (01:38) correct 14% (02:07) wrong based on 195 sessions

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The formula for the surface of a sphere is $$S=4πr^2$$. Two lead balls have radii 3 inches and 6 inches, respectively. A third ball has surface area equal to the sum of the surface areas of the two smaller balls. What is the radius, in inches, of the third ball?

(A) $$3\sqrt{10}$$
(B) $$3\sqrt{5}$$
(C) $$36π$$
(D) $$45π$$
(E) $$180π$$

It's not really a hard question, but I got it wrong because I didn't take enough time to read carefully the question. So i'll just leave it here for others to avoid my mistake.
Good luck ya'll

PS: Difficulty is probably under 600, but couldn't edit the tags

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Intern  Joined: 23 Aug 2015
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Re: The formula for the surface of a sphere is S=4πr^2. Two lead balls  [#permalink]

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petocities
The correct answer is B.
The surface area of the bigger sphere is = 4π (3^2 +6^2) = 4πr^2
4π (9 + 36) = 4πr^2
45 = r^2
r = \sqrt{45}
= 3 \sqrt{5}
Intern  Joined: 26 Jul 2015
Posts: 18
Location: Chile
GMAT 1: 620 Q38 V37 GMAT 2: 690 Q49 V35 WE: Analyst (Consulting)
Re: The formula for the surface of a sphere is S=4πr^2. Two lead balls  [#permalink]

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erratic15 wrote:
petocities
The correct answer is B.
The surface area of the bigger sphere is = 4π (3^2 +6^2) = 4πr^2
4π (9 + 36) = 4πr^2
45 = r^2
r = \sqrt{45}
= 3 \sqrt{5}

Yeah, upon revising my calculations I got it right, but on my first time I stopped at 4π(9+36) = 180π. Since that's (E), I just selected it. That's the silly mistake that one has to avoid!
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Re: The formula for the surface of a sphere is S=4πr^2. Two lead balls  [#permalink]

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Can please somebody explain how the translation from /sqrt(45) --> 3*/sqrt(5) works?
I got this one right but only because I canceled the 3 obvious wrong ones and then estimated what value r approximately has to be
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Joined: 02 Sep 2009
Posts: 55150
Re: The formula for the surface of a sphere is S=4πr^2. Two lead balls  [#permalink]

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rasti12 wrote:
Can please somebody explain how the translation from /sqrt(45) --> 3*/sqrt(5) works?
I got this one right but only because I canceled the 3 obvious wrong ones and then estimated what value r approximately has to be

$$\sqrt{45}=\sqrt{9*5}=3\sqrt{5}$$

Hope it's clear.
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The formula for the surface of a sphere is S=4πr^2. Two lead balls  [#permalink]

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Can someone please explain why the SA of the third lead ball is not 180π? I calculated the first SA as 36π and the second as 144π then added them together. What am I missing to get to 45π as the third ball's SA? The formula for the surface of a sphere is S=4πr^2. Two lead balls   [#permalink] 07 Oct 2018, 08:18
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# The formula for the surface of a sphere is S=4πr^2. Two lead balls

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