MHT CET 2021 Math Solved Paper

Let height of a right circular cone =hcm and OA=rcmGiven, slant height of a right circular cone =3cm In △OAB,
∠BOA‌‌=90∘
(OB)2+(OA)2‌‌=(AB)2
[apply pythogoras theorem]
(h)2+(r)2‌‌=(3)2
r‌‌=√9−h2 . . . (i)
We know that, Volume of cone
=‌

π

3

πr2h
V=‌

π

3

(9−h2)×h
[‌ from Eq. (i), ‌r=√9−h2]
V=‌

π

3

(9h−h3)
‌

dV

dh

‌‌=‌

π

3

(9−3h2)
∴‌‌‌

dV

dh

‌‌=0⇒‌

π

3

(9−3h2)=0
⇒‌‌‌

h2

‌

‌‌=‌

9

3

=3⇒h=√3
‌

d2V

dh2

‌‌=‌

−6×h

3

<0
So, h=√3 of the cone for maximum volume