your calculation is correct.
is this the entire problem as written in the text?
The diagram shows a sector OAB of a circle, centre O and radius r cm. The length of the arc AB is p cm and angle AOB is Ѳ radian.
(a) Find Ѳ in terms of p & r.
(b) Deduce that the area of the sector is 1/2pr cm^2.
Given that r = 4.7 and p = 5.3, where each has been measured to 1 decimal place, find, giving your answer to 3 decimal places:
(c) The least possible value of the area of a sector.
(d) The range of possible values of Ѳ.
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I don’t understand this question properly. What is the least possible value? And what is the range?
By taking given r & p's value,
A = ½ * (4.7)^2 * (5.3/4.7) [Using A = 1/2 * r^2 * Ѳ]
= 12.455 cm^2
But book’s answer: 12.206 cm^2.
"Given that r = 4.7 and p = 5.3, where each has been measured to 1 decimal place"
That means the least possible value of r = 4.65 and the least possible value of p = 5.25
Now, 1/2 * p * r = 1/2 * 5.25 * 4.65 = 12.206 cm^2 ---> Book's answer
You know the least possible values of r and p. The maximum possible value of r = 4.74 and p = 5.34. Now can you find the range of values of theta?
I hope that helps.
ILoveMaths07.