Will fan and give medal.

The perimeter of a circular sector is 20 cm and the radius is increasing at 5 cm/s. At what rate is the sector changing when the radius is 10 cm. Also at what rate is the area changing when the radius is 10 cm.

Hi, Can anyone help me in this question. I don't know where should i start. Thanks.

Question

Will fan and give medal.

The perimeter of a circular sector is 20 cm and the radius is increasing at 5 cm/s. At what rate is the sector changing when the radius is 10 cm. Also at what rate is the area changing when the radius is 10 cm.

Hi, Can anyone help me in this question. I don't know where should i start. Thanks.

devonhoward15 · Answer

nice car

isaiah.feynman · Answer

Hmmm...

isaiah.feynman · Answer

The area of a sector is given as $$A = \frac{ r^{2} \theta }{2}$$

isaiah.feynman · Answer

To find the rate at which the area is increasing, you will have to implicitly differentiate the formula for area. Note that theta is in radians.

rahulmr · Answer

Thanks for that @Isaiah.Feynman , but don't you think i should use $$P=2*R+R*\theta $$

isaiah.feynman · Answer

I don't see how. I don't quite understand what is meant by "At what rate is the sector changing when the radius is 10cm"

isaiah.feynman · Answer

Also the perimeter would be $$P = (2+\theta)r$$

rahulmr · Answer

What i did was
$$p=2r+r \theta $$ since p=20cm
$$r=20/(2+\theta) $$ 

then i differentiate the equation and i got
$$-20/(2+\theta)^2 $$

rahulmr · Answer

now i don't know what should i do next

isaiah.feynman · Answer

I think you should differentiate first before plugging in numbers.

freckles · Answer

@Isaiah.Feynman is right
at what rate is the sector changing is very vague
what specifically are they talking about about the sector