KCET 2017 Math Solved Paper

Given that, radius of the sphere is
r=4
We now that, volume sphere is given by
V=

4

3

πr2 → (1)
and surface area of sphere is given by
S=4πr2 → (2)
Differentiating Eqs. (1) and (2) with respect to r, we get
‌

dV

dr

=‌

4

3

×3πr2=4πr2
And ‌

dS

dr

=4×2πr=8πr
So, ‌

dV

dS

=‌

dV/dr

dS/dr

=[‌

4πr2

8πr

]=‌

r

2

At r=4 cm, we get
(‌

r

2

)r=4=‌

4

2

=2cm3cm−2