Click here for First half of Exercise 16

Question 23: A plot is in the form of a rectangle having semi-circle-on as shown in the adjoining figure. and , find the area of the plot.

Answer:

Area of rectangle

Diameter of semi circle

Therefore Area of semi circle

Hence area of the park

Question 24: A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are and , find, the area of the playground. Take

Answer:

Area of rectangle

Radius of semicircle

Therefore Area of 2 semi circles

Therefore total area

Question 25: The outer circumference of a circular race-track is . The track is everywhere wide. Calculate the cost of leveling the track at the rate of paise per square meter. Take

Answer:

Let the outer radius

Circumference

Therefore inner radius

Therefore area of track

Cost of leveling

Question 26: A rectangular piece is long and wide. From its four corners, quadrants of radii have been cut. Find the area of the remaining part.

Answer:

Area of the rectangle

Area of quadrants

Therefore Remaining area

Question 27: Four equal circles, each of radius , touch each other as shown in the adjoining figures. Find the area included between them. Take

Answer:

Area of the square

Area of quadrants

Therefore Remaining area

Question 28: Four cows are tethered at four corners of a square plot of side , so that they just cannot reach one another. what area will be left ungrazed?

Answer:

Area of the square

Area of quadrants

Therefore Remaining area

Question 29: A road which is wide surrounds a circular park whose circumference is . Find the area of the road.

Answer:

Let the radius of the park

Circumference of park

Therefore

Outer radius

Therefore area of the road

Question 30: Four equal circles, each of radius a, touch each other. show that the area between the is . Take

Answer:

Area of rectangle = (2a) \times (2a) = 4a^2

Area of quadrants

Therefore Remaining area

Question 31: Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions . Find the area of the remaining cardboard. Take

Answer:

Area of board

Area of two cut outs

Remaining area

Question 32: In the adjoining figure, a square is inscribed in a quadrant of a circle. If , find the area of the shaded region.

Answer:

Given: , is a square

Therefore Radius

Hence area of quadrant

Area of square

Therefore shaded area

Question 33: In the adjoining figure, is a right angled triangle in which and . Semi-circles are described on and as diameters. Find the area of the shaded region.

Answer:

Area of small semi circle with diameter

Area of large semi circle with diameter

Area of large semi circle with diameter

Area of

Therefore shaded area

Question 34: In the adjoining figure, and is mid-point of . Semi-circles are drawn on and as diameters. A circle with center touches all the three circles. Find the area of the shaded region.

Answer:

Total area of large semi circle

Area of two smaller semi circles

Let the radius of the small circle

Therefore,

Therefore area of small circle

hence the shaded area

Question 35: In the adjoining figure, the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is and of the smallest is , find i) the length of the boundary ii) the area of the shaded region.

Answer:

Length of boundary

Therefore shaded area

Question 36: In the adjoining figure, is the center of a circular arc and is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. Take

Answer:

Therefore Radius

Perimeter

Shaded region

Question 37: In the adjoining figure, there are three semicircles, and having diameter each, and another semicircle having a circle with diameter are shown. Calculate: (i) the area of the shaded region (ii) the cost of painting the shaded region at the rate of , to the nearest rupee.

Answer:

i) Area of shaded area

ii) Therefore cost of painting shaded area

Question 38: In the adjoining figure and are two diameters of a circle perpendicular to each other and is the diameter of the smaller circle. lf , find the area of the shaded region.

Answer:

Area of larger circle

Area of smaller circle

Therefore shaded region

Question 39: In the adjoining figure, is a quadrant of a circle with center and radius . If is , find the area of the i) quadrant an ii) shaded region.

Answer:

i) Area of quadrant

ii) Area of shaded region

Question 40: For each of the two opposite corners of a square of side , a quadrant of a circle of radius is cut. Another circle of radius is also cut from the center as shown in the figure. Find the area of the remaining shaded portion of the square. Take

Answer:

Shaded area

Question 41: Find the area of the shaded region in the adjoining figure, if , and is center of the circle. Take

Answer:

Therefore radius of the circle

Hence the shaded area

Question 42: In the adjoining figure, is a square of side . If is a quadrant of a circle with center , then find the area of the shaded region. Take

Answer:

Shaded area

Question 43: In the adjoining figure, is a rectangle, having and . Two sectors of have been cut off. Calculate: i) the area of the shaded region ii) the length of the boundary of the shaded region.

Answer:

Area of the shaded region

Perimeter

Question 44: A circle is inscribed in an equilateral triangle is side , touching its Sides as shown in the adjoining figure. Find the radius of the inscribed circle and the area of the shaded part.

Answer:

Area of

Let the radius of the circle

Therefore

Therefore area of circle

Therefore shaded area

Question 45: In the adjoining figure, shows the cross-section of railway tunnel. The radius of the circular part is . If , calculate: (i) the height of the tunnel (ii) the perimeter of the cross-section (iii) the area of the cross-section.

Answer:

i) Height of tunnel

ii) Perimeter

iii) Area of cross-section