The short and long hands of a clock
are 6 cm and 8 cm long, respectively.
Then, the sum of the distance travelled
by their tips in 1 day is (take a = 22/7]
Answers
Answer:
In 2 days, the short hand will complete 4 rounds.
∴ Distance moved by its tip = 4(circumference of a circle of radius 4 cm)
=4×(2×
7
22
×4)cm=
7
704
cm
In 2 days, the long hand will complete 48 rounds.
∴ Distance moved by its tip = 48(circumference of a circle of radius 6 cm)
=48×(2×
7
22
×6)cm=
7
12.672
cm
Hence,
sum of distances moved by the tips of two hands of the clock
=(
7
704
+
7
12672
)cm = 1910.85cm
The sum of the distance traveled by their tips in 1 day is 1281.12 cm
Explanation:
Given:
1. The short hand of a clock is 6 cm.
2. The long hand of a clock is 8 cm.
To find:
The sum of the distance traveled by their tips in 1 day
Formula:
Circumference of a circle is 2πr
We know that,
1 day = 24 hours
==> Short completes their one rotation in 12 hours
==> So, For one day short hand complete their rotation in 24 hours
==> 1 rotation = 12 hours
==> 2 rotation = 24 hours
Circumference of a circle for short hand = 2 × 2πr
==> Radius = 6cm
==> Short hand = 2 × 2π(6)
==> Short hand = 4 × π(6)
==> Short hand = 24π
==> π = 3.14
==> Short hand = 24(3.14)
==> Short hand = 75.36
==> Long hand complete their one rotation in 1 hour
==> For per day, long hand complete 24 rotation in 24 hours
==> 1 rotation = 1 hour
==> 24 rotation = 24 hour
Circumference of a circle for Long hand = 2πr
Circumference of a circle for Long hand = 24 × 2πr
==> Radius = 8cm
==> Long hand = 24 × 2π(8)
==> Longt hand = 48 × π(8)
==> Long hand = 384π
==> π = 3.14
==> Long hand = 384(3.14)
==> Long hand = 1205.76
Short hand + long hand = 75.36 + 1205.76
75.36 + 1205.76 = 1281.12 cm
The sum of the distance traveled by their tips in 1 day is 1281.12 cm