In , a sector is bounded by radii and and arc . If m = 90 ° and PX = 6 m, find the exact area of the sector.
A)9
B)12
C)3
D)36

Question

In  , a sector is bounded by radii  and  and arc  . If m  = 90 ° and PX = 6 m, find the exact area of the sector.
A)9 
B)12 
C)3 
D)36

Quizplus · Accepted Answer

First, we need to find the radius of the sector. We know that PX = 6 m and m 11ebfb55_24c0_f7f7_9d86_bf4a5c420f2f_TBX8811_11 = 90°, so we can use the Pythagorean theorem to find the radius:

Radius^2 = PX^2 + XO^2
Radius^2 = 6^2 + 6^2
Radius^2 = 72
Radius = √72 = 6√2

Next, we need to find the area of the sector, which is given by:

Area = (m/360°) x πr^2

Substituting in the values we know:

Area = (90/360) x π(6√2)^2
Area = (1/4) x 36π
Area = 9π

Thus, the exact area of the sector is 9π, which corresponds to choice A.

In , a Sector Is Bounded by Radii