The volume of a sphere with radius r is 4/3*r^3 and the surface area

Question

The volume of a sphere with radius r is  \frac{4}{3}πr^3  and the surface area is  4πr^2 . If a spherical balloon has a volume of 972π cubic centimeters, what is the surface area of the balloon in square centimeters?

(A) 324
 (B) 729
 (C) 243π
 (D) 324π
 (E) 729π

Bunuel · Answer

The volume of a sphere with radius r is \(\frac {4}{3} \pi r^3\) and the surface area is \(4 \pi r^2\). If a special ballon has a volume of \(972\pi\)cubic centimeters, what is the surface area of the ballon in square centimeters?

A. 324
B. 729
C. \(243\pi\)
D. \(324\pi\)
E. \(729\pi\)

Given: \(Volume=\frac {4}{3} \pi r^3=972\pi\) --> \(r=9\);

So, the surface area would be \(4 \pi r^2=324\pi\).

Answer: D.

For more on 3-D geometries check this: math-3-d-geometries-102044.html

Hope it helps.

thangvietname · Answer

we do not have to remember the formular for volume and surface area of a ball. is that right?

that is good

reto · Answer

As far as I know, we do not have to remember it. Economist also supports that:

"If you find these formulas hard to remember, don't sweat it. If a sphere is tested in the GMAT, the problem always supplies the relevant formula."

TimeTraveller · Answer

r^3 = 972*3/4 = 729.
so, r = 9.
Surface area = 4(pi)(9)^2 = 324 (pi). Ans (D).

gmatchile · Answer

We need the radius (r) of the sphere, to form the answer to the question posed.

They tell us that the volume of the sphere is 972π

So 4/3πrexp3 = 972π, we simplify the πs on both sides, we get:
4/3rexp3 = 972

Then: rexp3 = (3 x 972)/4

rexp3 = (3 x 972)/4

rexp3 = (3 x 243 x 4)/4

Simplifying the 4, we have

rexp3 = 3 x 243

rexp3 = 3 x 3 x 81

rexp3 = 9 x 9exp2

rexp3 = 9exp3

then r = 9

So the surface of the sphere is:

4πrexp2, substituting r = 9, we have

4π9exp2 = 4π81 = 324π

Answer D

CrackverbalGMAT · Answer

Hi all !
Lets see how we can solve this without a lot of calculations :)

Spherical balloon has a volume of 972π.
So we have the value of 4/3π\(r^3 \)

4/3 π \(r^3\) = 972 π

At this stage, you can factor out and cancel the π from both sides of the equation.
Also, factor out 972 with 4 so that we have
1/3 * (\(r^3\)) = 243
=> \(r^3\) = 3 * 243 = 3* \(3^5\) = \(3^6\)
=> r = \(3^2\)
I will keep the radius as an exponent since we are going to deal with radius again as \(r^2\) for the surface area.
I would like to see if I could use any exponent laws while computation to make it easier.

Now we get to the surface area which is 4 π \(r^2\) computation
I usually try to factor or factor and multiply in the last step with the questions-

So 4 π \(r^2\) = 4 π \((3^2)^2\)

The correct answer has to contain a π and a unit digit of 4*\(3^4\) which is 4*1 or 4
The only such answer choice is D.

Hope you are clear !

Devmitra Sen
GMAT Mentor

Hope you are clear ! Devmitra Sen GMAT Mentor

yannichc · Answer

are we really expected to know that 9^3 = 729?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The volume of a sphere with radius r is 4/3*r^3 and the surface area

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The volume of a sphere with radius r is 4/3*r^3 and the surface area

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards