Circumference & Area of a Circle | Areas Related to Circles | Assessment | English | Grade 10

If the circumference and half the area of a circle are equal, then the radius of the circle is _____________

• 2 units

• 14 units

• 2π units

• 4 units

Answer explanation

We know that the circumference of a circle = 2πr and, Area of a circle = πr² According to the question, 2πr = ½ πr² Or, 4r = r² So, r = 4 units Hence the correct answer is option 4.

Tags

CCSS.7.G.B.4

The diameter of two circles are 12 m and 16 m respectively. The radius of the circle having area equal to the sum of the areas of the two circles is equal to _______.

• 24 m

• 10 m

• 15 m

• 20 m

Answer explanation

Circle 1: Diameter = 12m, radius = r1 = 6m Circle 2: Diameter = 16 m, radius = r2 = 8 m Area of circle 1 = π r1² = 36π Area of circle 2 = π r2² = 64π Sum of areas of circle 1 and circle 2 = 36π + 64 π = 100 π So If radius of new circle is R, then, πR² = 100 π R² = 100, i.e., R = 10 m Hence the correct answer is option 2.

A bullock cart wheel of radius 35 cm makes 500 revolutions in 15 minutes. What is the speed of the bullock cart?( Take π =22/7)

• 2.2 kmph

• 4.4 kmph

• 5.5 kmph

• 8.8 kmph

Answer explanation

Distance travelled in 1 revolution = 2πr radius = r = 35 cm So, Distance travelled in 1 revolution = 2 x (22/7) x 35 = 220 cm Number of revolutions in 15 minutes = 500 Distance travelled in 15 minutes = 500 x 220 cm = (500 x 220)/1000 = 1.1 km Since speed = distance/ time Speed of the cart = 1.1 / (15/60) = 1.1 x (60/15) = 4.4 kmph Hence, the correct answer is option 2.

Deepak runs with a speed of 13.2 kmph. If he completes 10 rounds around a circular playground in an hour, find the area of the playground. ( Take π =22/7)

• 69,300 m²

• 277,200 m²

• 138,600 m²

• 13860 m²

Answer explanation

Deepak's speed = 13.2 kmph In one hour, he covers a distance of 13.2 km = 10 rounds of the playground. Distance covered in 1 round = 13.2/10 = 1.32 km = 1320m Distance covered in 1 round = perimeter of circular playground = 2πr, where r is radius of playground. 2πr = 1320 m r = 1320/2π = 660 x (7/22) = 210 m Area of circle = πr² Area of playground = π (210)² = (22/7) (210)² = 138,600 m² Hence the correct answer is option 3.

Tags

CCSS.7.G.B.4

The hour hand and minute hand of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips (in metres) in 48 hours . ( Take π = 3.14 )

• 9.55 m

• 19.1m

• 76.4 m

• 38.2 m

Answer explanation

Radius of hour hand = 4 cm Distance covered in 1 round = 2πr = 8π cm Hour hand completes 1 round in 12 hours So distance covered in 48 hours = 4 x 8 π = 32π cm Radius of minute hand = 6 cm Distance covered in 1 round = 2πr = 12π cm Minute hand completes 1 round in 1 hour So distance covered in 48 hours = 48 x 12 π = 576π Sum of the distance travelled by the hour hand and the minute hand in 48 hrs = 32π + 576π = 608π cm = 608(3.14) cm = 1909.12 cm = 19.0912 m or 19.1 m ( after rounding off) Hence the correct answer is option 2.

Tags

CCSS.3.MD.D.8