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 area of the smaller sector POQ, correct to 3 decimal places.
Options - A) 7.065 cm^2 B) 7.069 cm^2 C) 7.071 cm^2
D) 10.07 cm^2
Part b-
Choose the option that is the perimeter of the smaller sector POQ, correct to 3 significant figures. (The perimeter of the sector is the distance around all the edges of the sector.)
Options - A) 7.069 cm B) 7.07 cm C) 10.7 cm D) 10.712 cm
for part a i thinks its 7.069cm squred
but i don't knw what part b is
I got a different answer for Part a. I first figured the area of the complete circle [A = pi(r^2)]. Then I found one fourth of the complete area.
For Part b, you first need the total circumference of the circle. Using the formula C = pi (2r), I get 18.8496 cm. One "side" of the sector then is 18.84/4 = 4.7124.
Add 4.7124 to the other two sides of the sector to find the total perimeter.
To find the area of the smaller sector POQ, we can use the formula for the area of a sector of a circle:
Area = (θ/360) * π * r^2
Where θ is the central angle of the sector and r is the radius of the circle.
In this case, since the angle POQ is a right angle, it is 90 degrees or π/2 radians. Also, the radius of the circle is given as 3 cm.
Let's substitute these values into the formula:
Area = (90/360) * π * (3^2) = (1/4) * π * 9 ≈ 7.069 cm^2
So your answer for Part a is correct. It is indeed 7.069 cm^2.
Now let's move on to Part b, finding the perimeter of the smaller sector POQ.
The perimeter of a sector is the sum of the arc length and the lengths of both radii forming the sector.
Arc length = (θ/360) * 2 * π * r
In this case, considering the same angle POQ of 90 degrees or π/2 radians and the radius of 3 cm, we can substitute the values into the arc length formula:
Arc length = (90/360) * 2 * π * 3 ≈ 1/2 * π * 3 = π*(3/2) = 4.712 cm
Now, to find the perimeter, we need to add the lengths of the two radii:
Perimeter = Arc length + 2 * radius = 4.712 + 2 * 3 = 4.712 + 6 = 10.712 cm
The correct answer for Part b is therefore 10.712 cm, option D.