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The circumference of a circle exceeds its diameter by 45 cm. Find the circumference of the circle.
Given, the circumference of a circle exceeds its diameter by 45 cm.
⇒ Circumference of circle = Diameter of circle + 45
Let ‘d’ = diameter of the circle
⇒ Circumference = d + 45 → eqn1
And we know, Circumference of a circle = 2πr → eqn2
Where r = radius of circle
Also, we know that the radius of the circle is half of its diameter.
Put value of circumference in equation 1 from equation 2
⇒ 2πr = d + 45 → eqn4
Put value of r in equation 4 from equation 3
⇒ πd = d + 45
⇒ πd – d = 45
⇒ (π – 1)d = 45 (taking d common from L.H.S)
On rearranging, we get
⇒ d = 21 cm
Therefore, the diameter of the circle is 21 cm.
Thus, the radius of the circle
⇒ r = 10.5 cm
Now put the value of r in equation 2, we get
= 66 cm
The circumference of the circle is 66 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.]