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

Commented by liki last updated on 03/Mar/20

$$...helpmeplzqnsno.5,7and9$$

Commented by liki last updated on 03/Mar/20

$$...plzhelpme.....$$

Answered by Kunal12588 last updated on 03/Mar/20

Commented by Kunal12588 last updated on 03/Mar/20

$$\frac{{dr}_2}{dt}=1cm/s,\frac{{dr}_1}{dt}=2cm/s$$$$A_{shaded}=\pi r_2^2-\pi r_1^2$$$$\Rightarrow A_{shaded}=\pi (r_2^2-r_1^2)$$$$\Rightarrow \frac{dA}{dt}=2\pi (r_2\times \frac{{dr}_1}{dt}-r_1\times \frac{{dr}_2}{dt})$$$$\Rightarrow \frac{dA}{dt}=2\pi (r_2\left(1\right)-r_1\left(2\right))$$$$\Rightarrow \frac{dA}{dt}=2\pi (r_2-2r_1)$$$$when{r}_1=8cm,r_2=12cm$$$$\frac{dA}{dt}=2\pi (12-16)$$$$\frac{dA}{dt}=-8\pi cm/s$$

Answered by Kunal12588 last updated on 03/Mar/20

Commented by Kunal12588 last updated on 03/Mar/20

$$\frac{r}{h}=\frac{12}{18}$$$$\Rightarrow r=\frac{2h}{3}$$$$V=\frac{1}{3}\pi r^{2}h$$$$\Rightarrow V=\frac{1}{3}\pi \times \frac{4}{9}{h}^3$$$$\Rightarrow V=\frac{4}{27}\pi h^3$$$$\Rightarrow \frac{dV}{dh}=\frac{4}{9}\pi h^2\times \frac{dh}{dt}$$$$\Rightarrow \frac{dV}{dh}=\frac{4}{9}\pi \times 36\times \frac{dh}{dt}$$$$\Rightarrow 2=16\pi \frac{dh}{dt}$$$$\Rightarrow \frac{dh}{dt}=\frac{1}{8\pi }cm/s$$

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