Percentage Q59

59.	The volume of the sphere Q is 3764% less than the volume of sphere P and the volume of sphere R is 1927% less than that of sphere Q. By what % is the surface area of sphere R less than the surface area of sphere P?

	A.	77.77 %
	B.	87.5 %
	C.	75 %
	D.	67.5 %

Answer – (C)
Solution:
Let the volume of sphere P be 64 parts.
Therefore volume of sphere Q =64−(3764)% of 64=64−37=27 parts.
The volume of R =27−(1927)*27=27−19=8 parts.
Volume ratio:
=P:Q:R=64:27:8
Radius ratio:
=P:Q:R=4:3:2
The surface area will be 16:9:5
Surface area of R is less than the surface area of sphere P
16k−4k=12k
Now, 12k16k*100=75%
Thus surface area of sphere R is less than the surface area of sphere P by 75 %