# How do i do this maths question??

posted by .

A sector of a circle with radius r cm contains an angle of θ radians between the bounding radii. Given that the perimeter of the sector is 7cm, express θ in terms of r and show that the area is r/2(7-2r)cm square. Hence, find the maximum area of this sector as r varies.

I have already done the first part of the question, i only don't know how to do the "hence...". Please help, Thanks!

• How do i do this maths question?? -

arc length = a = rѲ
Then P = 2r + rѲ
7 = 2r + rѲ
Ѳ = (7-2r)/r

Let the area of the sector be A
by ratios
A/(pir^2) = Ѳ/(2pi)
A = (r^2)Ѳ/2
or
Ѳ = 2A/r^2

then 2A/r^2 = (7-2r)/r
solving for A after cross-multiplying and simplifying
A = (7r-2r^2)/2 or r/2(7-r) as required

second part:
A = (7/2)r - r^2 from above
dA/dr = 7/2 - 2r
= 0 for a max/min of A
2r - 7/2 = 0
r = 7/4
so Ѳ = (7 - 2(7/4))/(7/4)
Ѳ = 2 (how nice)

so max area = (r^2)(Ѳ)/2
= (49/16)(2)/(7/4)
= 7/2

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### maths

please can some one help me..? Part a - O is the centre of the circle, and P , Q are points on the circumference of the circle, with the angle POQ being a right angle. The radius of the circle is 3 cm. Choose the option that is the
2. ### trigonometry

please check my answers. 1.Find the area of the sector of a circle. r=11.8cm, theta-pi/7 radians I got 31.2cmsquared 2.Find the radius of a circle in which a central angle of pi/6radian determines a sector of area 76square meters. …
3. ### trig

In a circle of radius 12 inches, a sector is formed by a central angle of pie/4 radians. Find the area of the sector to the nearest hundredth of a square inch.
4. ### TRIG HELP ASAP

I really need help on this problem. A sector has area of 15 in^2 and central angle of 0.2 radians. Find the radius of the circle and arc length of the sector
5. ### pre-calc

Find an angle between 0 and 2ð that is coterminal with the given angle. -8pi/3 A sector of a circle has a central angle of 60°. Find the area of the sector if the radius of the circle is 3 mi.
6. ### trigonometry

A sector AOB of a circle, centre O, radius r cm, where the acute angle AOB is theta radians. Given that the perimeter of the sector is 14 cm and that the area of the sector is 10 cm^2, evaluate r and theta.
7. ### Trig

Find the area of a sector with the given central angle θ in a circle of radius r. θ = 90°, r = 6 cm
8. ### maths

find the angle of a sector of a circle of radius 35cm is 288' find the perimeter of the sector
9. ### Algebra 2

If the arc length of a sector in the unit circle is 3π/2 what is the measure of the angle of the sector?
10. ### MATHS

CALCULATE A PERIMETER OF A SECTOR OF A CIRCLE OF RADIUS 7CM WHICH SUBTENDS ANGLE 6ODEGREE AT A CENTRE.

More Similar Questions