In preparation for a party, a spherical ballon is blown up from a diameter of 10cm to a diameter of 30cm. by?

Question

how many times has its surface area increased?


please answer it clear and explain .

Answer 1

Well, to make it simple, you would assume that the balloon is spherical, and that the little tube-y bit that you blow into is of negligible surface area.

The surface area of a sphere is given by 4x(pi)xradius(squared)

The radius the begin with is 5cm
Afterwards it is 15cm

Therefore the surface area before is:
4 x (pi) x 25

and the surface afterwards is:
4 x (pi) x 225

Now, the magnitude of change can be given by:

Surface area afterwards (divided by) Surface area before

Which equals:

4 x (pi) x 225
----------------
4 x (pi) x 25

You cancel the 4s and the (pi)s, leaving yourself with:

225
-----
25

Which = 9

Therefore the surface area has increased by 9 times.

(you get the same result if you leave the 4(pi) there, too).