Question

the height of cone is 9cm and volume is 48π find diameter of base​

Answer 1

$\huge\mathcal{Answer:}$

Given

Height (h)=9 cm

Volume=48π cm^3

Volume of the circular cone

$= \frac{1}{3} \pi {r}^{2} h$

volume of the right circular cone =48πcm^3

$\frac{1}{3} \pi {r}^{2} h = 48\pi$

$\frac{1}{3} \times {r}^{2} \times 9 = 48$

$3 {r}^{2} = 48$

${r}^{2} = \frac{48}{3} = 16$

${r}^{2} = \sqrt{16}$

$r = 4cm$

$diametre \: of \: the \: base \: = 2 \times r = 2 \times 4 = 8cm$

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

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

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