The hour and minute hands of a clock are 4 cm and 6 cm long respective

1.	The hour and minute hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in 2 days.
Answer» Length of the hour hand is 4 cm, which describes the radius of the path inscribed by the hour hand. Length of the minute hand is 6 cm, which describes the radius of the path inscribed by the minute hand. The circumference of the path inscribed by the hour hand = 2 π r C = 2 × (22/7) × 4 C = 176/7 cm The hour hand makes 2 revolutions in one day. Therefore distance covered by the hour hand in 2 days = (176/7) × 2 × 2 = 100.57 cm The distance covered by the minute hand in 1 revolution = 2 π r C = 2 × (22/7) × 6 C = 264/7 As we know, the minute hand makes 1 revolution in one hour. In 1 day, it makes 24 revolutions. In 2 days, it makes 2 × 24 revolutions. The distance covered by the minute hand in 2 days = 2 × 24 × (264/7) = 12672/7 = 1810.28 cm The sum of the distances travelled by the hour and minute hands in 2 days = 1810.28 + 100.57 = 1910.85 cm

The hour and minute hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in 2 days.

Answer»

Length of the hour hand is 4 cm, which describes the radius of the path inscribed by the hour hand.

Length of the minute hand is 6 cm, which describes the radius of the path inscribed by the minute hand.

The circumference of the path inscribed by the hour hand = 2 π r

C = 2 × (22/7) × 4

C = 176/7 cm

The hour hand makes 2 revolutions in one day.

Therefore distance covered by the hour hand in 2 days = (176/7) × 2 × 2

= 100.57 cm

The distance covered by the minute hand in 1 revolution = 2 π r

C = 2 × (22/7) × 6

C = 264/7

As we know, the minute hand makes 1 revolution in one hour.

In 1 day, it makes 24 revolutions.

In 2 days, it makes 2 × 24 revolutions.

The distance covered by the minute hand in 2 days = 2 × 24 × (264/7)

= 12672/7

= 1810.28 cm

The sum of the distances travelled by the hour and minute hands in 2 days = 1810.28 + 100.57

= 1910.85 cm