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

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."

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

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

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

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