Question-83524

Question Number 83524 by liki last updated on 03/Mar/20

Commented by liki last updated on 03/Mar/20

\dots h e l p m e p l z q n s n o . 5, 7 a n d 9

Commented by liki last updated on 03/Mar/20

\dots p l z h e l p m e \dots . .

Answered by Kunal12588 last updated on 03/Mar/20

Commented by Kunal12588 last updated on 03/Mar/20

\frac{{d r}_{2}}{d t} = 1 c m / s, \frac{{d r}_{1}}{d t} = 2 c m / s

A_{s h a d e d} = π r_{2}^{2} - π r_{1}^{2}

\Rightarrow A_{s h a d e d} = π (r_{2}^{2} - r_{1}^{2})

\Rightarrow \frac{d A}{d t} = 2 π (r_{2} \times \frac{{d r}_{1}}{d t} - r_{1} \times \frac{{d r}_{2}}{d t})

\Rightarrow \frac{d A}{d t} = 2 π (r_{2} (1) - r_{1} (2))

\Rightarrow \frac{d A}{d t} = 2 π (r_{2} - 2 r_{1})

w h e n r_{1} = 8 c m, r_{2} = 12 c m

\frac{d A}{d t} = 2 π (12 - 16)

\frac{d A}{d t} = - 8 π c m / s

Answered by Kunal12588 last updated on 03/Mar/20

Commented by Kunal12588 last updated on 03/Mar/20

\frac{r}{h} = \frac{12}{18}

\Rightarrow r = \frac{2 h}{3}

V = \frac{1}{3} π r^{2} h

\Rightarrow V = \frac{1}{3} π \times \frac{4}{9} h^{3}

\Rightarrow V = \frac{4}{27} π h^{3}

\Rightarrow \frac{d V}{d h} = \frac{4}{9} π h^{2} \times \frac{d h}{d t}

\Rightarrow \frac{d V}{d h} = \frac{4}{9} π \times 36 \times \frac{d h}{d t}

\Rightarrow 2 = 16 π \frac{d h}{d t}

\Rightarrow \frac{d h}{d t} = \frac{1}{8 π} c m / s