Question

A horse take \(2\frac{1}{2}\)seconds to complete a round around a circular field. If the speed of the horse was 66m/sec, then the radius of the field is,
Given [\(\pi=\frac{22}{7}\)]

• A. 25.62 m
• B. 26.52 m
• C. 25.26 m
• D. 26.25 m

Answer 1

The Correct Option is D

To find the radius of the circular field, we start by using the relationship between speed, distance, and time. The formula for speed is given by:

Speed = Distance / Time

The distance covered in one full round of the circular field is the circumference of the circle, which can be calculated using:

Circumference of a circle = \(2\pi r\)

where \(r\) is the radius of the circle. Given that the speed of the horse is 66 m/sec and the time taken is \(2\frac{1}{2}\) seconds, we first convert the time into an improper fraction:

\(2\frac{1}{2}\) seconds = \(\frac{5}{2}\) seconds

Substituting the values for speed and time into the formula:

66 m/sec = \(\frac{2\pi r}{\frac{5}{2}}\)

Solve for \(r\) (radius):

\(66 = \frac{4\pi r}{5}\)

Multiply both sides by 5:

\(330 = 4\pi r\)

Divide both sides by \(4\pi\):

\(r = \frac{330}{4\pi}\)

Substitute the value of \(\pi\) as \(\frac{22}{7}\):

\(r = \frac{330 \times 7}{4 \times 22}\)

Calculate the expression:

\(r = \frac{2310}{88}\)

Simplify:

\(r \approx 26.25\) m

Thus, the radius of the field is 26.25 m.