Question 1

A circular road runs rounds a circular ground. If the difference between the circumference of the outer circle and the inner circle is 66 meters, the width of the road is?

Accepted Answer

Let outer radius be R and inner radius be r. Then from question 2πR - 2πr = 66 ⇒ 2π (R-r) = 66 ⇒ (2 x 22)/7 x (R - r) = 66 ∴ (R-r) = (66 x 7) / 44 = 10.5 m

Question 2

The inner circumference of a circular race track, 14 m wide is 440 m . Then the radius of the outer circle is?

Accepted Answer

Circumference of a circular = 2πr ⇒ 2 x (22 / 7) x r = 440 ⇒ r = [440 x (7/22) x (1/2)] = 70 m ∴ Radius of outer circle = (70 + 14) m = 84 m

Question 3

The ratio of the radii of two circle is 1:3 the radio of their areas is?

Accepted Answer

The Radio of areas = area of first circle : area of 2nd circle = πr2 / π(3r)2 = πr2/ 9 πr2 = 1/9 = 1: 9

Question 4

The Area of a square is 50 sq. units. Then the area of the circle drawn on its diagonal is?

Accepted Answer

Area = (Diagonal)2 / 2 = 50 ⇒ Diagonal = 10 units ∴ Radius of required circle = 5 units Its area = [π x (5)2 ] cm2 = 25π units2

Question 5

A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6: 5 . The smaller side of the rectangle is?

Accepted Answer

Perimeter of rectangle = Circumference of circle = 2πr =2 x ( 22/7 ) x 42 = 264 cm Now perimeter of rectangle = 2 x ( 6a + 5a ) ⇒ 2 x (6a + 5a) = 264 ⇒ a = 12 Smaller side of rectangle = 5a = 60 cm

Question 6

If 88 m wire is required to fence a circular plot of land, then the area of the plot is?

Accepted Answer

Circumference of circular plot= 88 m ⇒ 2 x (22/7) x r = 88 ⇒ r = 88 x (7/22) x (1/2) = 14 m Now area = πr2 =( 22/7) x 14 x 14 m2 = 616 m2

Question 7

If the circumference of a circle is increased by 50%, then its area will be increased by?

Accepted Answer

Original circumference = 2πr New circumference = (150 /100) x 2 πr = 3πr 2πR = 3πr ⇒ R = 3r/2 Original area = πr2 New area = πR2 = π9r2 / 4 = 9πr2/4 Increase in area = (9πr2/4 ) - (πr2) = (5/4) πr2 Req. increase per cent = [{(5/4) πr2} / {πr2}] x 100 = 125 %

Question 8

If a regular hexagon is inscribed in a circle of radius, r then its perimeter?

Accepted Answer

Length of each side of hexagoan = radius of circle ∴ its perimeter = 6r

Question 9

Four horses are be tethered at four concern of a square plot of side 63 meters, so that they just cannot reach one another. The area left ungrazed is?

Accepted Answer

Area left ungrazed = [(63 x 63) - (4 x 1/4 x 22/7 x (63/2)2] m2 = (63 x 63 - (99 x 63)/2 ) m2 = 63 x (63 - 99/2) m2 = 850.5 m2

Question 10

The circumferences of two concentric are 176 m and 132 m respectively. what is the difference between their radii?

Accepted Answer

∵ 2πR - 2πr = (176-132) ⇒ 2π(R-r) = 44 ⇒ R-r = ( 44 x 7 )/ (2 x 22) = 7 m

Question 11

The diameter of a circle is 105 cm less than the circumference. What is the diameter of the circle?

Accepted Answer

∵ πd-d = 105 cm ⇒ (π -1 ) d = 105 cm ⇒ [(22/7)-1] x d = 105 cm ∴ d = (7/15) x 105 cm = 49 cm

Question 12

The area of the sector of a circle, whose radius is 12 meters and whose angle at the centre is 42, is?

Accepted Answer

Area of the sector = [(22/7) x 12 x 12] x [42°/360°] m2 = 52.8 m2

Question 13

In a circle of radius 21 cm an arc subtends an angle of 72° at the centre. The length of the arc is?

Accepted Answer

Arc length = 2πr (θ° / 360°) = 2 x (22/7) x 21 x (72° / 360°) cm = 26.4 cm

Question 14

The area of sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm is?

Accepted Answer

Area of sector = ( arc length x radius ) / 2 cm2 = (3.5 x 5 ) / 2 = 8.75 cm2

Question 15

A rectangular carpet has an area of 120 sq. m and a perimeter of 46 m . The length of its diagonal is?

Accepted Answer

Let length = a metres and breadth = b metres Then, 2(a+b)= 46 ⇒ (a+b) =23 and ab =120 ∴ Diagonal = √a2 + b2 √(23)2-2 x 120 √289 = 17 m

Question 16

Radhika runs along the boundary of a rectangular park at the rate of 12 km/hr and completes one full round in 15 minutes. If the length of the park is 4 times its breadth , the area of the park is?

Accepted Answer

Speed = 12 x (5/18) m/sec =10/3 m/sec there4; perimeter = (10/3) x 15 x 60 m=3000 m ∵ 2( a + 4a) = 3000 m ⇒ a = 300 m So, length = 1200 m and breadth = 300 m ∴ Area = (1200 x 300 ) m2 = 360000m2

Question 17

If D,E and F are respectively the midpoint of the sides BC , CA and AB of a Δ ABC and the area of Δ ABC = 36m 2. Then area of Δ DEF is?

Accepted Answer

Area of a triangle formed by joining the mid point of the sides of the triangle is 1/4th of area of the original triangle . So area of Δ DEF = 36/ 4 = 9 m2

Question 18

A rectangular carpet has an area of 60 sq. m. Its diagonal and longer side together equal 5 times the shorter side, The length of the carpet is?

Accepted Answer

Let the longer side = l, shorter side = b and diagonal = d Then, area of rectangular carpet = l x b = 60 ....(1) And from question d + l = 5b ⇒ d = 5b - l ...(2) ⇒ d2 = 25b2 + l2 - 10 x lb ⇒ l2+ b2 = 25b2 + l2 - 10 x lb ⇒ l2+b2 = 25b2 + l2 - 10 x 60 ⇒ 24b2 = 600 ∴ b = √25 = 5 m √ l = 60 / b = 60 / 5 = 12 m

Question 19

In Δ ABC ,sides BC = 10 cm and height AD = 4.4 cm. If AC = 11 cm. Then altitude BE equals?

Accepted Answer

We know that area of triangle = ( base x height ) / 2 So area of triangle = (BC x AD) / 2 = (AC x BE) / 2 ⇒ (10 x 4.4) / 2 = (11 x h) / 2 ⇒ h= (10 x 4.4)/11 = 4 cm

Question 20

The cross section of a canal is a trapezium in shape . If the canal is a trapezium in shape. If the canal is 10 meters wide at the top and 6 meters wide at bottom and the area of cross section is 640 sq. meters The depth of canal is?

Accepted Answer

Cross section area = 1/2 x ( a + b ) x d where a and b are the parallel sides, d is the perpendicular distance between them. ⇒ 1/2 x ( a + b ) x d = 640 ⇒ d = (640 x 2) / 16 = 80m

Area Questions