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

Show Answer

Official Answer

D

(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?

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

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

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