Question

Please answer the question below..

Answer 1

The length of x in the sector is 7.08 cm.

How to find area of a sector?

area of a sector = ∅ / 360 × πr²

where

• r = radius

Therefore,

area of a sector = 60 / 360 × π × 10²

area of a sector = 60 / 360 × π × 100

area of a sector = 6000 / 360 π

Hence,

area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 =  26.1666666667 = 26.2 cm

Hence,

26.2 = 60 / 360 × 3.14 × x²

x² = 26.2 / 0.52333333333

x = √50.0637261552

x = 7.07557064836

x = 7.08 cm

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Answer 2

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of big sector = (60/360) * π(10)² = (50π /3) cm²

Area of small sector = (60/360) * π(x)² = (x²π /6) cm²

Unshaded area = (x²π /6) cm²

Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6

Shaded area = unshaded area

(100π - x²π) /6 = (x²π /6) cm²

x = 7.07

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

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