Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q. 38 (page 541)

See the following figure. Find the area

of the shaded region enclosed in a semicircle of diameter 10 inches. The length of the chord PQ is 8 inches.

Short Answer

Expert verified

The area of the shaded part is15.27sq.units

Step by step solution

01

Given information

We are given a figure

02

Use Pythagoras theorem to find the length of QR

By Pythagoras theorem

PQ2+QR2=PR282+QR2=10264+QR2=100QR2=36QR=6

03

Find the area of Semicircle and triangle

Area of semicircle

Ks=πr22Ks=π(5)22Ks=39.27sq.units

Area of triangle

Kt=ab2Kt=8(6)2Kt=24sq.units

04

Find the area of shaded region

Area of shaded region is

Kr=Ks-KtKr=39.27-24Kr=15.27sq.units

05

Conclusion

The area of shaded region is 15.27sq.units

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Area of an ASA Triangle If two angles and the included side are given, the third angle is easy to find. Use the Law of Sines to show that the area K of the triangle with side aand angles A, B, and C is

K=a2sinBsinC2sinA

Landscaping Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one

position on a flat path from the tree is 30°, and from a second position 40 feet farther along this path it is 20°. What is the height of the tree?

an object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.

(a) Develop a model that relates the distance d of the object from its rest position after t seconds.

(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.

Given values:m=25,a=10,b=0.7,T=5

A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?

A 22-foot extension ladder leaning against a building makes a 70° angle with the ground. How far up the building does the ladder touch?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free