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3 years ago

Shaded area is 54 pi cm squared. Find X

Mathematics

2 answers:

EleoNora [17]3 years ago

8 0

Answer:

x = 3π/4 radians = 135°

Step-by-step explanation:

The area of a sector of central angle α is ...

A = (1/2)r²α

Filling in the given values, we can find the central angle to be ...

54π cm² = (1/2)(12 cm)²x

x = (54π)/(72) = 3/4π . . . . radians

x = 135°

Tanzania [10]3 years ago

7 0

Answer:

Step-by-step explanation:

The shaded area is a sector of the circle. The formula for determining the area of a sector is expressed as

expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 12 cm

θ = x°

Area of sector = 54π

Therefore,

54π = x/360 × π × 12²

54π × 360 = x × π × 12

19440π = 144πx

Dividing through by π, it becomes

19440 = 144x

x = 19440/144

x = 135°

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