Circle Geometry

Let the length of rectangle = 8x cm and breadth = 7x cm. Perimeter of rectangle = circumference of circle = 2(8x + 7x) = 60 x = 2 Then, length = 16 cm and breadth = 14 cm. Now, area of the rectangle = 224 cm².

The sector has taken out from a circle. Therefore, radii of both will be same. So, area of sector = (pie*r²*angle)/360 degree = 154/6 = (22*r²*60)/7*360 = 154/6 r = 7 cm Therefore, radius of circle = 7 cm.  

Though the formulation is correct but the unit of area is sq. units. So it is the incorrect option as asked in the question.

This is the correct answer. Since a semicircular garden with its diameter as one of the lengths of rectangular house is to be constructed, it means length of the house = diameter of garden Area of the house = 2200 sq. m Breadth of the house is = 11 m Area of the house = length * breadth             2200 sq. m = length * 11 m                 (2200/11) m = length                      200 m = length Length = diameter = 200 m Radius of the semicircular garden is = diameter/2 = (200/2) m                                                         = 100 m

Ans. 100 m

This is the right answer as:- Diameter of semicircular silver wire = 70 cm Radius of semicircular silver wire = 70/2 = 35 cm Circumference of the gold ring = circumference of the semicircular silver wire (given in the question) 2 * pi * radius of gold ring = pi * radius of the silver wireradius of gold ring = (pi * radius of the silver wire)/(2 * pi) radius of gold ring                                    = 35 cm/2                                    = 17.5 cm

Ans. 17.5 cm

Diameter of old circle = 2 r Radius = r Area = pi * radius * radius Radius of new circle = 2 r Area of new circle = pi * 2 r * 2r                      => pi * 4 * radius * radius Ratio = area of old circle / area of new circle            => 1/4

Ans. 4 * pi * r * r ; 1/4

Distance covered in 4 rounds = 42 m Distance covered in 1 round = 42 / 4                                                    =10.5 m Distance covered in 1 round = Circumference of the circle                  = >2 * pi * radius = 10.5 m       radius =10.5 m / (2 * pi) = 1.7 m Area of the circular shape = pi * radius * radius                                                 =>3.14 * 1.7 * 1.7                                              = 9.1 sq. m. Ans. 9.1 sq. m

Area of square sheet = 169 sq.cm Side x side = 169 sq.cm Side = 13 cm Since, square is divided into four circles, so radius of each circle = 1/4 of side of the square = 13/4 = 3.25 cm Circumference of each circle = 2 x pi x radius 2 x 3.14 x 3.25 cm = 20.41 cm Ans. 20.41 cm

In programming, identifiers cannot begin with a digit. '4th semester' starts with the number 4, making it invalid. Valid identifiers like 'Area_of_circle', 'Pi-value', and 'Count2' start with letters or underscores.

Of all the triangles inscribed in a semi-circle, with the diameter as base, the one with the greatest area is the one with the largest altitude (the radius), i.e. the isosceles triangle. Thus, the area = 1/2 * 2r * r = r². Hence, option (1) is correct.

Let the length of rectangle be L. Then, 2(L + 5.5) = 35 Or 2L = 24 L = 12 m Area of rectangle = 12*5.5 = 66 sq m So, area of circle = area of rectangle = 66 sq. m

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Wardrop's formula for roundabout capacity: C = (284 * w * (1 + e/w) * (1 - p/3)) / (1 + w/l). Given w=14, e=8.4, l=35, p = 1000/2000 = 0.5. C = (284 * 14 * (1 + 8.4/14) * (1 - 0.5/3)) / (1 + 14/35) = (3976 * 1.6 * 0.833) / 1.4 = 5298 / 1.4 = 3784. The closest value is 3700.

Area of circle with radius 6 cm =  $\pi$(6)² = 36$\pi$ cm². Area of circle with radius 8 cm = _^$\pi$ (8)² = 64_^$\pi$ cm².  Total area of both circles = 36_^$\pi$ cm² + 64_^$\pi$cm² = 100_^$\pi$ cm².  So, the radius of the new circle be R. _^$\pi$R² = 100_^$\pi$cm² R² = 100 cm² = R _{^{$\Rightarrow$}} 10 cm.