Math: Test 6

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by briana145
Last updated 5 years ago

Discipline:
Math
Subject:
Geometry
Grade:
10,11,12

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Math: Test 6

The points P and Q lie on a circle, with centre o and radius 8 cm, such that POQ=59°.Find the area of the shaded segment of the circle contained between the arc PQ and the chord [PQ]

STEP 1

First, I changed 59° to radians. To do this, I multiplied π/180º by 59 which equals 1.029.Then I found the area of the sector by using the Area of a sector formula. A=(1/2)×8²×(1.029)A=32.95

VocabularySector: The area between two radii and the connecting arc of a circle.Radius: A straight line from the center to the circumference of a circle or sphereChord: A straight line joining the ends of an arc

Next, I split the triangle in half so I can find the area of the right triangle. But first, I need to find another side.To do this I will be using SOHCAHTOA. Cos(29.5)=A/8A/8=0.87A=0.87×8A=6.96=7

Step II

Pythagorean Theorema2 + b2 = c2*2=squared*

Step III

Then I used the pythagorean theorem to find the missing side. a2+7^2=8^2a^2= 15 The square root of 15 is 3.9=4

Step IV

Then, I used the formula for area of triangle to find the area.A= 7*4/2A=15I then double that to get the area of the entire triangle.15*2=30

In order to find the area of the shaded section, you subtract 32.95 from 30 to get 2.95 as the answer.

Step V

By: Briana Walker

Test 6, #1


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