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Surface Areas And Volumes

Question
CBSEENMA10008650
Wired Faculty App

A chord of circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :

(i) Minor segment
(ii) Major sector.

Solution

Here, we have
r = 10 cm, and ө = 90°


Area of  sector (OAPBO)
equals space πr squared space equals space straight theta over 360 equals space 3.14 space straight x space 10 space straight x space 10 space straight x space 10 space straight x space 90 over 360 equals space 3.14 space straight x space 5 space straight x space 5 equals space 78.5 space cm squared
Area of  incrementAOB
     equals space 1 half straight r squared space space sin space straight theta space equals space 1 half space straight x space 10 space straight x space 10 space straight x space sin space 90 degree equals space space 1 half space straight x space 10 space straight x space 10 space straight x space 1 equals space 50 space cm squared

Now,
(i) Let APB A is the given minor segment, then Area of minor segment (APBA)
= Area of sector (OAPBO) - area of ∆ (AOB)
= 78.5 cm2 - 50 cm2
= 28.5 cm2.
(ii) Area of major sector
= Area of circle Area of sector OAPBO
= (πr2 - 78.5) cm2
= (3.14 × 10 × 10 - 78.5) cm2
= (314 - 78.5) cm2 = 235.5 cm2

Some More Questions From Surface Areas and Volumes Chapter

The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumference of two circles.

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles. 

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Tick the correct answer in the following: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units    (D) π units
(C) 4 units    (D) 7 units.

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