Question

The drawing shows a semicircular window separated into 3 sections of . Red Green Green Approximately how many of the glass are red? The window a diameter of 18 units

Answer 1

Answer:

$\frac{45π}{2} \: units^{2} \: ≈ \: \boxed{70.7 \: units²}$

______________________

The correct option is 70.7

Step-by-step explanation:

Since the green and red make a semicircle, the total measure must be 180°.

Since the two green sectors are both 40°.

The red must add up with the green sectors to total 180°.

This means that:

red sector + 80° = 180°.

–80° –80.

red sector = 100°.

To find the area of a sector, we must first understand the area of the circle itself which is πr², where r is the radius.

Since a full circle is 360°.

(360° / 360°)( πr² ) will be the area.

Or in radians: (2π rad / 2π rad)( πr² ).

From here, we can create the formula:

Area of a sector = ( n° / 360° ) ( πr² ). Where n is the measure or the sector in degrees, and r is the radius.

You may also know that the diameter is twice the measure of the radius.

This means that if we are given a diameter of 18 units from the problem, the radius will be 18/2 or 9 units.

Lastly, all we have to do is substitute all this information to find the area of sector.

Area of the red sector = ( n° / 360° ) ( πr² ).

Area of the red sector =

( (100°) / 360° ) ( π(9)² ).

Area of the red sector = ( 5 / 18 ) ( 81π )

Area of the red sector = ( (5)(81π) / 18 )

Area of the red sector = ( (405π) / 18 )

Area of the red sector = ( 45π / 2 ) units²

Area of the red sector =

(141.371669412.. units²) / 2

Area of the red sector =

70.6858347058.. units²

Area of the red sector ≈

70.7 units²

Answer 2

Um let me figure this out right now!