Problems based on S R Theta Formula

Here we will solve two different types of problems based on S R Theta formula. The step-by-step explanation will help us to know how the formula ‘S is Equal to R’ is used to solve these examples.

Problems based on S R Theta Formula:

1. The large hand of a big clock is 35 (thirty-five) cm long. How many cm does its extremity move in 9 (nine) minutes?

Solution:The angle traced by the large hand in 60 minutes = 360°

                         = 2π Radians.

Therefore, the angle traced by the large hand in 9 minutes

                         = [(2π/60) × 9] Radians

                         = 3π/10 Radians

Let s be the length of the arc moved by the tip of the minutes hand, then

     s = rθ

or, s = [35 × (3π/10)] cm

or, s = [35 ∙ (3/10) ∙ (22/7)] cm

or, s = 33 cm.

2. Assuming the distance of the sum from the observer to be 9,30,00,000 miles and the angle subtended by the diameter of the sun at the eye of the observer to be 32', find the diameter of the sun.


Let O be the observer, C the center of the sun and AB be the diameter of the sun.

Then by problem, OC = 9,30,00000 and ∠AOB = 32' = (32/60) × (π/180) radian.

If we draw a circle with center at 0 and radius OC then the arc intercepted by the diameter AB of the sun on the drawn circle will be very nearly equal to the diameter AB and of the sun (since OC is very large ∠AOB is very small).

Therefore, using the formula s = rθ we get,

AB = OC × ∠AOB, [Since, s = AB and r = OC]

= 9,30,00000 × 32/60 × π/180 miles

= 9,30,00000 × 32/60 × 22/7 × 1/180 miles

= 8,67,686 miles (approx.)

Therefore, the required diameter of the sun = 8,67,686 miles (approx.).

3. At what distance does a man, 5½ feet in height, subtend an angle of 20”?


Let, MX be the height of the man and this height subtends an angle 20" at the point O where OX = r feet (say).

Therefore, ∠MOX = 20" = {20/(60 × 60)}° = 20/(60 × 60) = π/180 radian.

Clearly, ∠MOX is very small; hence, MX is very small compared to OX.

Therefore, if we draw a circle with center at O and radius OX, then the difference between arc length M’X and MX will be very small. Hence, we can take, arc M'X = MX = height of the man = 5½ feet = 11/2 feet.
Problems based on S R Theta Formula
Now, using the formula, s = rθ we get,

r = OX

or, r = s/θ

or, r = (Arc M’X)/θ

or, r = MX

or, r = (11/2)/[20/(60 × 60) × (π/180)]

or, r = (11 × 60 × 60 × 180 × 7)/(2 × 20 × 20) feet.

or, r = 10 miles 1300 yards.

Therefore, the required distance = 10 miles 1300 yards.

 Measurement of Angles

11 and 12 Grade Math

From Problems based on S R Theta Formula to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Shifting of Digits in a Number |Exchanging the Digits to Another Place

    May 19, 24 06:35 PM

    Shifting of Digits in a Number
    What is the Effect of shifting of digits in a number? Let us observe two numbers 1528 and 5182. We see that the digits are the same, but places are different in these two numbers. Thus, if the digits…

    Read More

  2. Formation of Greatest and Smallest Numbers | Arranging the Numbers

    May 19, 24 03:36 PM

    Formation of Greatest and Smallest Numbers
    the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

    Read More

  3. Formation of Numbers with the Given Digits |Making Numbers with Digits

    May 19, 24 03:19 PM

    In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

    Read More

  4. Arranging Numbers | Ascending Order | Descending Order |Compare Digits

    May 19, 24 02:23 PM

    Arranging Numbers
    We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

    Read More

  5. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 19, 24 01:26 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More