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

//Multiple Choice

What is the formula for the area of a sector of a circle? {
~ πr² ÷ 360
~ 2πr × θ/360
~ r² × θ/360
= πr² × θ/360
}

What is the angle subtended at the center of a semicircle? {
~ 90°
~ 360°
= 180°
~ 60°
}

How many degrees does the minute hand of a clock move in 20 minutes, as discussed in Video 3? {
~ 30°
= 120°
~ 60°
~ 90°
}

If a cake is divided into 6 equal parts, what is the angle of each sector? {
~ 90°
~ 45°
~ 120°
= 60°
}

What is the area of each piece of the cake divided into six equal parts as mentioned in Video 2, if the diameter of the cake is 12 cm? {
= 18.85 cm²
~ 28.85 cm²
~ 12.85 cm²
~ 20.85 cm²
}

What is the value of π used in the clock problem? {
~ 3.1415
~ 22/7
= 3.14
~ 3
}

If a sector has an angle of 72° and the radius is 10 cm, find the area of the sector using π\=3.14. {
~ 63.28 cm²
~ 36 cm²
~ 125.6 cm²
= 88.12 cm²
}

In the disc example from Video 2, what is the difference between the two shaded areas of the sectors? {
~ 25.5 cm²
= 38.5 cm²
~ 28.5 cm²
~ 50.5 cm²
}

In which video is the example about dividing a cake into six equal parts mentioned? {
~ Video 1
= Video 2
~ Video 3
~ None of these
}

What is the remaining angle of a major sector when the minor sector subtends 120°? {
= 240°
~ 180°
~ 360°
~ 120°
}

//True or False

The total angle at the center of a circle is 360°. {T}

A semicircle subtends 90° at its center. {F}

The area of a sector is directly proportional to the angle subtended by it at the center. {T}

In the disc example, the larger sector's radius is 7 cm. {F}

The formula for the area of a minor sector is (θ/360) × πr². {T}

The angle formed by the minute hand in 10 minutes is 60°. {T}

The area of a major sector can be found by subtracting the area of the minor sector from the total area of the circle. {T}

A cake divided into six parts will have each part subtending 120° at the center. {F}

The radius of the cake in the first example is 6 cm. {T}

The value of π used in the clock problem is 3.1415. {F}

//Numericals

Calculate the area of a sector where θ \= 45° and r \= 10 cm. Use π \= 3.14. {
~ 39.25 cm²
~ 78.50 cm²
~ 157 cm²
~ 314 cm²
}

A circle has a radius of 7 cm, and a sector subtends 72° at the center. Find the area of the sector. Use π \= 3.14. {
~ 14.14 cm²
~ 28.28 cm²
~ 56.52 cm²
~ 113.04 cm²
}

A clock’s minute hand is 14 cm. Calculate the area of the sector it covers when it moves 90°. Use π \= 3.14. {
~ 77 cm²
~ 153.86 cm²
~ 307.72 cm²
~ 615.44 cm²
}

A disc has radii 10 cm and 5 cm, and a sector subtends 30° at the center. Find the area of the region between the two arcs. Use π \= 3.14. {
~ 19.625 cm²
~ 39.25 cm²
~ 78.5 cm²
~ 157 cm²
}

Find the area of a sector when the radius is 12 cm and the angle subtended is 120°. Use π \= 3.14. {
~ 75.36 cm²
~ 150.72 cm²
~ 301.44 cm²
~ 602.88 cm²
}

//Fill in the blanks

The formula for the area of a circle is ______. {
~ 2πr²
= πr²
~ 2πr
~ r²
= πr²
}

The angle subtended by the sectors of a cake divided into six equal parts is ______ degrees. {
~ 30
= 60
~ 90
~ 120
= 60
}

The angle subtended by the minute hand in one minute is ______ degrees. {
= 6
~ 5
~ 10
~ 12
= 6
}

The shaded area of the disc in the example is ______ square centimeters. {
~ 28.5
= 38.5
~ 25.5
~ 50.5
= 38.5
}

The radius of the smaller sector in the disc problem is ______ cm. {
~ 10
= 7
~ 5
~ 14
= 7
}

The total degrees at the center of a circle are ______. {
= 360
~ 180
~ 90
~ 240
= 360
}

The remaining area of the clock apart from the minor sector is ______ square centimeters. {
~ 120.33
= 209.33
~ 104.66
~ 304.33
= 209.33
}

A semicircle subtends ______ degrees at its center. {
~ 90
= 180
~ 360
~ 60
= 180
}

The area of a sector depends on its ______. {
~ Radius
~ Angle
= Both (Radius and Angle)
~ None
= Both (Radius and Angle)
}

The area of a sector depends on the radius of the circle and the ______ subtended by the sector. {
~ Diameter
= Angle
~ Circumference
~ Area
= Angle
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Minor sector -> 360° - minor sector angle
=Semicircle -> Subtends 180°
=Total angle at center -> 360°
=Major sector area -> πr² - minor sector area
=Sector formula -> (θ/360)πr²
}



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