Area of a sector of angle 150° of a circle with radius 21 cm is _____. (Take π = 22/7)

We know that the Area of a sector of a circle = θ/360 πr² Given, θ = 150⁰ , r = 21 cm So, Area of sector = 150/ 360 π(21)² = 1155/2 = 577.5 cm² Hence the correct answer is option 1.

The radius of a circle is 10 cm. If the area of a sector of the circle is 100 cm², then the area of its corresponding major sector is ____________. (Take π = 3.14)

Given : radius of circle = 10 cm Area of minor sector = θ/360 πr² = 100 cm² Area of circle = π r² = 100π Area of Major sector = π r² ─ θ/360 πr² = 100π ─ 100 = 100(3.14) ─ 100 = 314 ─ 100 = 214 cm² Hence the correct answer is option 2

A sector is cut off from a circle of radius 21 cm. The angle of the sector is 120⁰. The area of the remaining part of the circle is _______.

Area of circle = π r² = 22/7 × 21 × 21 = 1386 cm² Area of sector = θ/360 π r² = 120/360 × 1386 cm² = 1/3 × 1386 = 462 cm² So, Area of Remaining portion = Area of Circle ─ Area of sector = 1386 cm² ─ 462 cm² = 924 cm² Hence the correct answer is option 3.

A circular disc of radius 6 cm is divided into three sectors with the angles of sectors measuring 170⁰, 100⁰ and 90⁰, respectively. The ratio of the areas of these sectors is ________.

Given : Circular disc is divided into 3 sectors. θ₁ = 170⁰, θ₂= 100⁰, θ₃ = 90⁰ , r = 6 cm Area of minor sector = θ/360 πr² Area of sector 1 = 170/360 × 36 π Area of sector 2 = 100/360 ×36 π Area of sector 3 = 90/360 × 36 π Hence, Ratio of areas of sectors = 170:100:90 = 17:10:9 Hence the correct answer is option 4.

The length of the minute hand of a clock is 14 cm. The area swept by the minute hand between 7:00PM to 7:40PM is _______.

Radius of minute hand = 14 cm Angle described by minute hand in 1 minute = 6⁰ Between 7.00 pm to 7.40 pm , there are 40 minutes. Angle described by minute hand in 40 minutes = 40 × 6⁰ = 240⁰ We know, Area of a sector = θ/360 πr² Area of sector = 240/360 × 22/7 × 14² = 410.67 cm² Hence the correct answer is option 2.

In the given figure, PQRS is a rectangle. If PQ = 21 cm and QR = 14 cm, what is the area of the shaded part z?

Given : PQ = 21 cm, QR = 14 cm Since PQRS is a rectangle, ∠ PSR = ∠ QRS = 90⁰ PS = QR = 14 cm and PQ = SR = 21 cm Area of rectangle PQRS = PQ x QR = 21 x 14 = 294 cm² Radius of quadrant X = PS = 14 cm Area of quadrant X = 90/360 × Π × 14² = 154 cm² Radius of quadrant Y = SR - PT = 21 - 14 = 7 cm Area of quadrant Y = 90/360 × Π × 7² = 38.5 cm² Hence, Area of the part z = Area of rectangle PQRS ─ Area of quadrant X ─ Area of quadrant Y = 294 ─ 154 ─ 38.5 = 101.5 cm² Hence, the correct answer is option 1