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Question
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
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Solution
Let r and R be the lengths of the short and long hands of the clocks, respectively.
Length of the short hand of the clock, r = 4 cm
Distance travelled by the tip of the short hand in 12 hours = \[2\pi r\] = 2 × 3.14 × 4 = 25.12 cm
∴ Distance travelled by the tip of the short hand in 24 hours = 2 × 25.12 = 50.24 cm
Length of the long hand of the clock, R = 6 cm
Distance travelled by the tip of the long hand in 1 hour =\[2\pi R\]
2 × 3.14 × 6 = 37.68 cm
∴ Distance travelled by the tip of the long hand in 24 hours = 24 × 37.68 = 904.32 cm
Now,
Sum of the distances travelled by their tips in 24 hours
= Distance travelled by the tip of the short hand in 24 hours + Distance travelled by the tip of the long hand in 24 hours
= 50.24 cm + 904.32 cm
= 954.56 cm
Hence, the sum of the distances travelled by their tips in 24 hours is 954.56 cm.
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It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
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The coordinates of the centroid of ΔEHJ are ______.
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
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