Answer:
(a) 3364π cm^2
or we can write it as
10568.32 cm^2 to the nearest hundredth.
(b) 5476π cm^2.
or we can write it as
17203.36 cm^2 to the nearest hundredth.
Step-by-step explanation:
(a)
If we draw lines from the centre of the sphere to either side of the dotted line which is marked as 40 cm long , we have an inverted isosceles triangle whose hypotenuse = the radius of the sphere.
So radius^2 = 21^2 + ( 1/2*40)^2 (by Pythagoras theorem).
r^2 = 841
r = 29 cm.
So the surface area of the sphere = 4 pi r^2
= 4 * π * 841
= 3364π cm^2.
(b)
If we draw similar lines as in (a) we have an inverted isosceles triangle with base 24 and height (72-r).
So r^2 = 12^2 + (72 - r)^2
---> r^2 = 144 + 5184 - 144r + r^2
--> 144r = 144 + 5184
--> r = 37
So, the surface area of the sphere
= 4π(37)^2
= 5476π cm^2.
