Question

The minute hand of a clock is 10 cm long. How far does the tip of the hand move in 20 minutes

• A. $\frac{3}{20}cm$
• B. $\frac{3\pi}{20}cm$
• C. $\frac{20}{3}cm$
• D. $\frac{20\pi}{3}cm$

Answer 1

The Correct Option is D

The minute hand rotates across two-thirds of a radian or 120° in 20 minutes. The formula provides the distance travelled by the tip of the hand since the minute hand's length is 10 cm.

I = r θ = 10x2π/3 = 20π/3 cm.

The distance between two locations on the circumference of any circle is known as the arc length. It is consistently regarded as a circumference. Angle created between two line segments connecting a point to the terminus of an arc is known as the subtended angle.

The Arc Length Formula is frequently used to calculate the length of the curved line that makes up an arc. The length of an arc is the distance traversed by a circle's curved line. If a straight line and two endpoints of a circle are compared, the straight line will always have a shorter length. Depending on the arc's central angle's unit, many formulae can be used to calculate an arc's length. The centre angle is frequently measured in radians or degrees. It is well known that the arc length formula for circles equals times circle radius.

Arc length formula in radians can be as arc length = θ x r

Here θ is in radian.

Arc length = θ x (π/180) x r

Where θ is in degree, here L = length of an Arc, θ = is central angle of Arc and r = radius of circle.

The arc length of a circle can be measured based on the unit of the center angle of the arc. The arc length formula in radians is:

Arc Length = θ × r

Here, L = Arc Length, θ = Center angle of the arc in radians, and r = Radius of the circle