$CATEGORY: Maths - TicTacLearn/11. Areas related to circles/11. Areas related to circles--Area of Sector and Segment of a Circle

//Multiple Choice

The chord of a circle divides it into\: {
~ Radius and diameter
~ Sector and segment
= Major and minor segments
~ None of the above
}

What is the formula for the area of a segment of a circle? {
~ πr²
= (θ/360)πr² - (1/2) base × height
~ πrθ
~ (θ/360)πr²
}

In the hexagonal garden example, how many sectors are formed by dividing the circle? {
~ 5
= 6
~ 7
~ 8
}

In an equilateral triangle, each angle measures\: {
~ 45°
= 60°
~ 90°
~ 120°
}

he area of the minor segment in the right-angle example with radius 14 cm is\: {
= 55.86 cm²
~ 615.44 cm²
~ 60 cm²
~ 50 cm²
}

What is the angle formed at the center of a right-angle segment? {
~ 30°
= 90°
~ 120°
~ 180°
}

The area of the equilateral triangle in the hexagonal garden example is\: {
~ 209.52 m²
~ 217.92 m²
= 173.2 m²
~ 36.32 m²
}

The total area of the circle in the right-angle segment example is\: {
= 615.44 cm²
~ 36.32 cm²
~ 173.2 cm²
~ 209.52 cm²
}

In the segment area formula, what does sin(θ/2)⋅cos(θ/2) represent? {
~ Radius
~ Height of the triangle
= Area of the triangle (Actually represents 1/2 * base * height of the triangle, and together with r^2, it makes the area)
~ Central angle (Actually angle is theta, this is related to triangle's area calculation)
}

In the flower bed problem, what is the total area of all flower beds? {
~ 217.92 m²
= 209.52 m²
~ 36.32 m²
~ 173.2 m²
}

//True or False

The radius of a circle is half the length of its diameter. {T}

A segment of a circle is always a complete portion of the circle. {F}

The area of an equilateral triangle depends on the square of its side. {T}

The sum of the areas of the major and minor segments is equal to the area of the circle. {T}

The formula (θ/360)πr² gives the area of a segment. {F}

A hexagon divides a circle into six equal sectors, each with a central angle of 30°. {F}

The area of a circle depends only on its radius. {T}

The central angle for a right-angled sector is 90°. {T}

The formula 1/2 × base × height calculates the area of a sector. {F}

The area of a segment can be found by subtracting the area of a triangle from the area of the sector. {T}

//Numericals

Calculate the area of a sector with radius 7 cm and central angle 90° (π\=3.14). {
~ 153.86 cm²
= 38.47 cm²
~ 35 cm²
~ 50 cm²
}

Find the area of an equilateral triangle with a side of 10 cm. {
= 43.3 cm²
~ 50 cm²
~ 60 cm²
~ 25 cm²
}

Calculate the area of a minor segment in a circle with radius 14 cm and central angle 90° (π\=3.14). {
= 55.86 cm²
~ 65.32 cm²
~ 50.86 cm²
~ 59.44 cm²
}

If a hexagonal garden has a diameter of 40 meters, find the area of one flower bed. {
= 36.32 m²
~ 209.52 m²
~ 217.92 m²
~ 173.2 m²
}

A chord subtends a central angle of 120° in a circle of radius 10 cm. Find the area of the sector. {
= 104.67 cm²
~ 125.6 cm²
~ 100.5 cm²
~ 105 cm²
}

//Fill in the blanks

A chord divides a circle into a ______ and a ______ segment. {
= Major, Minor
~ Equal, Unequal
~ Inner, Outer
~ Small, Large
}

In the flower bed example, the radius of the garden is ______ meters. {
~ 10
= 20
~ 40
~ 30
}

The area of a triangle is calculated using the formula 1/2 × base × ______. {
~ Radius
= Height
~ Area
~ Side
}

In the formula for the area of a minor segment, the term subtracted from the area of the sector is the area of the ______. {
= Triangle
~ Circle
~ Segment
~ Sector
}

The area of an equilateral triangle is given by the formula (√3/4) × ______². {
~ Base
~ Radius
~ Height
= Side
}

The central angle of a right-angled segment is ______ degrees. {
~ 30
~ 120
~ 180
= 90
}

The height of the triangle in the minor segment formula is calculated using r⋅cos(θ/2). What is the missing trigonometric function? {
~ Sine
~ Tangent
~ Secant
= Cosine
}

The area of the sector in the hexagonal garden example is ______ square meters. {
~ 36.32
~ 173.2
~ 217.92
= 209.52
}

The radius of a circle is ______ the length of its diameter. {
~ Double
~ Equal
~ One-fourth
= Half
}

The area of each flower bed is ______ m². {
~ 209.52
~ 217.92
~ 173.2
= 36.32
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Sum of all angles in a triangle -> 180 degrees
=Formula for the area of the circle -> πr²
=Area of the sector OAPB in 2nd example -> 209.52 square meters
=Angle OAB in triangle AOB -> 60 degrees
=The shape of triangle AOB -> Equilateral
}



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