>> Elementary Mathematics >> Area and perimeter

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Contents:

- Elementary Mathematics
- Area and perimeter
- Circles
- Clocks
- Factorisation
- Geometry
- Height and Distance
- Indices and Surd
- LCM and HCF
- Loci and concurrency
- Logarithms
- Polynomials
- Quadratic Equations
- Quadrilateral and parallelogram
- Rational expression
- Real Analysis
- Rectangular and Cartesian products
- Set theory
- Simple and Decimal fraction
- Simplification
- Statistics
- Straight lines
- Triangle
- Trigonometric ratio
- Trigonometry
- Volume and surface area

51). If the radius of a circle is increased by 6%, find the percentage increase in its area.
Given that, a = 6 | ||||

52). The area of a sector of a circle is 77 sq cm and the angle of the sector is 45 degree. Find the radius of the circle.
Let the radius of circle = r cm According to the question, Area of sector = \( \Large 77 cm^{2} \) \( \Large \frac{\theta}{360 degree}\times \pi r^{2} \)=77 => \( \Large \frac{45 degree}{360 degree}\times \pi r^{2} \)=77 => \( \Large r^{2}=\frac{77\times 7\times 8}{22} \)=> r=14 cm | ||||

53). The wheel of an engine turns 350 times round its axle to cover a distance of 1.76 km. The diameter of the wheel is
Distance covered in 1 round | ||||

54). The ratio of the areas of the circumcircle and the incircle of a square is
Ratio of the areas of the circumcircle and incircle of a square | ||||

55). The circumferences of two circles are in the ratio 2 : 3. What is the ratio of their areas?
Let the radii of two circles are \( \Large r_{1} \) and \( \Large r_{2} \) respectively. | ||||

56). Consider the following statements Area of segment of a circle is less than area of its corresponding sector. Distance travelled by a circular Wheel of diameter 2d cm in one revolution is greater than 6d cm. Which of the above statements is/are correct?
We know that, area of segment (PRQP) = Area of sector (OPRQO)- Area of \( \Large \triangle OPQ\)
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57). The radius of a circle is so increased that its circumference increased by 5%. The area of the circle, then increases by
Increase in Circumference of circle = 5% | ||||

58). The area of a circle is increased by 22 sq cm when its radius is increased by 1 cm. Find the original radius of the Circle.
Let original radius be r. | ||||

59). What is the area of the larger segment circle formed by a chord of, length 5 cm subtending an angle of 90 degree at the centre?
In \( \Large \triangle AOB \),AO=OB=r[radius of circle] | ||||

60). A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30m/min, then the radius of the circular ground is \( \Large (take \ \pi = 22/7) \)
Let the radius of circular field = r m. |