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The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumferences of the circles.
Given Sum of the radius of the circles = 7 cm
the difference of their circumference = 8 cm
Let the radius one circle be ‘r1’ cm and other be ‘r2’ cm and circumference be ‘C1’ and ‘C2’ respectively.
Also, circumference of circle = 2πr
Where r = radius of the circle
C1 = 2πr1 and C2 = 2πr2
r1 + r2 = 7 → eqn1
C1 – C2 = 8 → eqn2
(Note: Her it is considered that r1>r2)
We can rewrite equation 2 as,
2πr1 – 2πr2 = 8
⇒ 2π(r1 – r2) = 8
(taking 2π common from L.H.S)
Put the value of r1 from equation 3 in equation 1
(taking 11 as LCM on R.H.S)
Put value of r2 in equation 3
(from equation 3)
(taking 22 as LCM on R.H.S)
(by putting value of r1)
= 26 cm
(by putting value of r2)
= 18 cm
The circumference of circles are 26 cm and 18 cm.
ABCD is a field in the shape of a trapezium, AD || BC, ∠ABC = 90° and ∠ADC = 60°. Four sectors are formed with centres A, B, C and D, as shown in the figure. The radius of each sector is 14 m.
Find the following:
(i) total area of the four sectors,
(ii) area of the remaining portion, given that AD = 55 m, BC = 45 m and AB = 30 m.
A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure. [Take π = 3.14.]