Loading [MathJax]/jax/output/HTML-CSS/jax.js

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Application Problems on Area of a Circle

We will discuss here about the Application problems on Area of a circle.

1. The minute hand of a clock is 7 cm long. Find the area traced out by the minute hand of the clock between 4.15 PM to 4.35 PM on a day.

Solution:

The angle through which the minute hand rotates in 20 minutes (i.e., 4:35 PM – 4:15 PM) is 2060 × 360°, i.e., 120°

Area Traced Out by the Minute Hand

Therefore, the required area = The area of the sector of central angle 120°

                                          = θ360 × πr2

                                          = 120360 × 227  × 72 cm2, [Since, θ = 120, r = 7 cm]

                                          = 13 × 22 × 7 cm2.

                                          = 1543 cm2.

                                          = 5113 cm2.


2. The cross section of a tunnel is in the shape of a semicircle surmounted on the longer side of a rectangle whose shorter side measures 6 m. If the perimeter of the cross section is 66 m, find the breadth and height of the tunnel.

Solution:

Let the radius of the secicircle be r m.

The Cross Section of a Tunnel

Then, the perimeter of the cross section

                                               = PQ + QR +PS + Semicircle STR

                                               = (2r + 6 + 6 + πr) m

                                               = (2r + 12 + 227 r) m

                                               = (12 + 2r + 227 r) m

                                               = (12 + 367 r) m

Therefore, 66m = (12 + 367 r) m

⟹ 66 = 12 + 367 r

⟹ 12 + 367 r = 66

367 r = 66 - 12

367 r = 54

⟹ r = 54 × 736

⟹ r = 212.

Therefore, PQ = Breadth of the tunnel = 2r m = 2 × 212 = 21 m.

And height of the tunnel = r m + 6 m

                                    = 212 m + 6 m

                                    = 212 m + 6 m

                                    = 332 m

                                    = 16.5 m.






10th Grade Math

From Application Problems on Area of a Circle 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. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  2. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  3. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More