Q21 of 180 Page 2

What is the radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm?

Diameter of first circle = d1 = 36 cm

Diameter of second circle = d2 = 20 cm


∴ Circumference of first circle = πd1 = 36π cm


Circumference of second circle = πd2 = 20π cm


Now, we are given that,


Circumference of circle = Circumference of first circle + Circumference of second circle


πD = πd1 + πd2


⇒ πD = 36π + 20π


⇒ πD = 56π


⇒ D = 56


⇒ Radius = = 28cm


More from this chapter

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19

Seema placed a lightbulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1 : 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; A = 105°, B = 100°, C = 70° and D = 85°.


(a) What is the measurement of angle A’?


(i) 105°


(ii) 100°


(iii) 70°


(iv) 80°


(b) What is the length of A'B'?


(i) 1.5 cm


(ii) 3 cm


(iii) 5 cm


(iv) 2.5 cm


(c) What is the sum of angles of quadrilateral A'B'C'D'?


(i) 180°


(ii) 360°


(iii) 270°


(iv) None of these


(d) What is the ratio of sides A’B’ and A’D’?


(i) 5: 7


(ii) 7: 5


(iii) 1: 1


(iv) 1 : 2


(e) What is the sum of angles of C’ and D’?


(i) 105°


(ii) 100°


(iii) 155°


(iv) 140°


 20

An electrician has to repair an electric fault on the pole of height 5 m. She needs to reach a point 1.3 m below the top of the pole to undertake the repair work (see figure)


(a) What is the length of BD?


(i) 1.3 m


(ii) 5 m


(iii) 3.7 m


(iv) None of these


(b) What should be the length of Ladder, when inclined at an angle of 60° to the horizontal?


(i) 7.4 m


(ii) m


(iii) 3.7 m


(iv) m


(c) How far from the foot of pole should she place the foot of the ladder? (i) 3.7


(ii) 2.14


(iii)


(iv) None of these


(d) If the horizontal angle is changed to 30°, then what should be the length of the ladder?


(i) 7.4 m


(ii) 3.7 m


(iii) 1.3 m


(iv) 5 m


(e) What is the value of B?


(i) 60°


(ii) 90°


(iii) 30°


(iv) 180°


 22

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. What is the probability that the selected ticket has a number which is a multiple of 5?

OR


A coin is tossed two times. Find the probability of getting atmost one head.


 23

Calculate the value of the expression


OR


If sin – cos = 0, then calculate the value of (sin4 + cos4).