Areas Related to Circles | Chapter Assessment | English | Grade 10

If the area of a circle is 314 cm², then what will be the circumference of the circle? (Take π = 3.14)

• 31.4 cm

• 62.8 cm

• 6280 cm

• 314 cm

Answer explanation

Given : Area of circle = 314 cm² We know that the perimeter or circumference of a circle = 2πr and the Area of a circle is πr² So, πr² = 314 cm² Or, r² = 314 / 3.14 = 100 cm² So, r = 10 cm Circumference of a circle = 2πr = 2 x 3.14 x 10 = 62.8 cm Hence the correct answer is option 2.

Tags

CCSS.7.G.B.4

If the area of a sector of a circle is 3.85 cm² and the angle of the sector is 36⁰, then find the radius of the circle. (Take π =22/7)

• 3.5 cm

• 3.85 cm

• 12.25 cm

• 1.1 cm

Answer explanation

Area of sector = 36/360 x π x r² = π/10 x r² 3.85 cm² = π/10 x r² 38.5 /π = r² r² = 12.25 cm² r = √12.25 = 3.5 cm Hence the correct answer is option 1

Tags

CCSS.HSG.C.B.5

In the given figure, O is the centre of a circle. If ∠ROQ = ∠MON = 60⁰, OR = 7 cm and OM = 21 cm, then the area of the shaded portion is _______. (Take π = 22/7)

• 231 cm²

• 25.67 cm²

• 205.33 cm²

• 256.67 cm²

Answer explanation

Area of sector ROQX = (θ/360) x π r² = (60/360) x π x 7² = π/6 x 7² = 25.67 cm² Area of sector MONY = (θ/360) x π r² = 60/360 x π x 21² = 231 cm² So, Area of Shaded portion = Area of sector MONY ─Area of sector ROQX = 231 ─ 25.67 = 205.33 cm² Hence the correct answer is option 3 If option 1 is chosen it will be incorrect as only area of segment MONY was taken. If option 2 is chosen it will be incorrect as only area of segment ROQX was taken. If option 4 is chosen it will be incorrect as while calculating the area of shaded portion the areas of the two segments was added instead of subtracted.

Tags

CCSS.HSG.C.B.5

If the area of sector AOBX of a circle is 100.25 cm², and the area of the enclosed triangle AOB is 78 cm², what will be the area of the enclosed segment?

• 22.25 cm²

• 78 cm²

• 12.25 cm²

• 32.25 cm²

Answer explanation

Area of sector = 100.25 cm² Area of enclosed Triangle = 78 cm² Area of segment = 100.25 ─ 78 = 22.25 cm² Hence the correct answer is Option 1.

Tags

CCSS.HSG.C.B.5

If a chord of a circle of radius 80 cm subtends an angle of 60° at the centre, then the area of the corresponding segment of the circle is _______. ( Take π = 3.14 )

• 581.12 cm²

• 7.264 cm²

• 1749.12 cm²

• 518.12 cm²

Answer explanation

Area of segment of a circle = r² [ θπ/360 ─ sinθ/2 cosθ/2] Given : r = 80 cm, θ = 60⁰ Area of segment of a circle = 80² [ 60π/360 ─ sin30 cos30] = 6400 [ π/6 ─√3/2 × 1/2] = 6400 [ 0.5233 ─ 0.4325 ] = 6400 x 0.0908 = 581.12 cm² Hence the correct answer is option 1.

Tags

CCSS.HSG.C.B.5

A square park has each side of length 100 m. At each corner of the park there is a flower bed in the form of a quadrant of a circle of radius 14 m. Find the area of the remaining part of the park.

• 9548 m²

• 9348 m²

• 9384 m²

• 9684 m²

Answer explanation

Area of square = 100 x 100 = 10000 m² Given : r = 14 m, θ = 90⁰ Area of 1 quadrant = 90π/360 x 14² = 154 m² Area of 4 Quadrants = 4 x 154 = 616 m² Area of remaining part of the park = Area of square ─ Area of 4 Quadrants = 10000 ─ 616 = 9,384 m² Hence the correct answer is option 3.

A field is in the shape of an equilateral triangle with each side equal to 50 m. At each vertex of the triangle a goat is tied. The first goat is tied with a rope of length 10 m. The second goat with a rope of length 15 m and the third with a rope of 20 m. Find the area of the field which cannot be grazed by the goats. (Take π = 3.14)

• 701.86 m²

• 963.51 m²

• 911.18 m²

• 1081.25 cm²

Answer explanation

Area of Triangle = √3/4 a² Given : a = 50 m, θ = 60⁰ Area of Triangle = √3/4 x 50² = 1081.25 m² Area of sector grazed by First Goat = 60/360 × 3.14 × 10² = 52.33 m² Area of sector grazed by Second Goat = 60/360 × 3.14 × 15² = 117.74 m² Area of sector grazed by Third Goat = 60/360 × 3.14 × 20² = 209.32 m² Total Area grazed by the goats = 52.33 + 117.74 + 209.32 = 379.39 m² So, Total ungrazed area = Area of triangle - area grazed by goats = 1081.25 ─ 379.39 = 701.86 m² Hence the correct answer is option 1.