Question

Which of the following could be used to calculate the area of the sector in the circle shown above?
π(5in)30 over 360
π(5in)230 over 360
π(30in)25 over 360
π(30in)5 over 360

Answer 1

the way I remember how to do this is first write down the area for the *whole* circle

Answer 2

can you do that ?

Answer 3

How would i know what the whole area is?

Answer 4

@phi

Answer 5

the formula for the area of a circle (people memorize this)
area= pi r^2

Answer 6

ok hold on let me solve that

Answer 7

can you write the area for the whole circle?

Answer 8

R^2= 25 then would i multiply 25x3.14?

Answer 9

you could, but all of your answer choices leave it pi, and write r^2 as 5^2
so just write

area of the whole circle is \( \pi 5^2 \)

Answer 10

Alright.

Answer 11

next, we are told the sector is 30 degrees.
Here is the idea: if the sector was 360 degrees, (all the way around), that would be the entire circle. If the sector was 180 degrees (half way round), that would be ½ of the circle
notice 180/360 is ½

in general we multiply by the fraction angle of sector / 360

Answer 12

so 30/360 right?

Answer 13

yes. so the final answer is
pi * 5^2 * 30/360
though they could write that in a different order. just look for pi, 5^2 and 30 up top and 360 in the bottom

Answer 14

so it is B right?

Answer 15

notice for a sector with angle = 90