Question

if the volume and the base area of a right circular cone are 48πcm^3 and 12πcm^2 respectively,then find height of cone.

Answer 1

Let || represent pie

||r^2 is area of the base(circle)
||r^2=12||
r^2=12 (pie cancel out)

Now, V of a cone = 1/3 || r^2 h
48|| = 1/3 || * 12 * h
48 = 1/3 * 12 * h (pie cancel out)
48 = 4 * h
h = 12cm

Answer 2

${\huge{\pink{\underline{\underline{\tt{\blue{Hey \: Mate!}}}}}}}$

Let the radius of the base of the right circular cone be r cm

h = 9cm

Volume = 48πcm³

$\dfrac{1}{3}$ πr²h = 48π

$\dfrac{1}{3}$r²h = 48

$\dfrac{1}{3}$ × r²h × 9 = 48

r² = $\dfrac{48×3}{9}$

r² = 16

r = √16

4cm

2r = 2(4) = 8cm

$\sf\orange{Hence, \: the \: diameter \: of \: the \: base \: of \: the \: right \: circular \: cone \: is \: 8cm}$

$\large\fbox\fcolorbox{red}{plum}{\color{navy}{Hope \: It \: Helps \: You}}$