Question
upstudy study bank question image url

EXERCISE 3
  1. Consider the diagram on the right.
    a) Find the values of and (leave your answers in surd form) and then
    calculate (correct to 2 decimal places).
    b) Round off and (to 2 decimal places) and then calculate (correct to 2
    decimal places).
    c) Compare the values of you got in 1.a) and ) and comment brlefly on
    the accuracy of your answers.
  2. The area of a circle is given by and the circumference is given by .
    If m, calculate:
    a) (correct to 2 decimal places) and use this value to calculate (corrcct to 2
    decimal places).
    b) but do not round off your answer before you calculate .
    c) Compare the values of you got in 2 (a) and and comment briefly on the
    accuracy of your answers.

Ask by Fleming Pollard. in South Africa
Jan 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Exercise 3 Solutions:
  1. Part 1:
    • a) meters, meters. Calculated meters.
    • b) Rounded and to 2 decimal places: meters, meters. Calculated meters.
    • c) Both values are the same, showing high accuracy.
  2. Part 2:
    • a) Radius meters. Area square meters.
    • b) Radius meters. Area square meters.
    • c) The area in part 2.b is slightly more accurate than part 2.a due to less rounding in the radius calculation.
Summary:
  • Part 1 involves solving for variables and and calculating with and without rounding, showing the impact of rounding on accuracy.
  • Part 2 calculates the radius and area of a circle given the circumference, demonstrating the effect of rounding on the final area calculation.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

To enhance your understanding, let’s dive into a little historical background about mathematics and its applications! Did you know that the ancient Greeks made significant contributions to geometry and circle calculations? For instance, Archimedes was one of the first to accurately calculate the circumference and area of a circle, laying the groundwork for future mathematicians. His methods used inscribed polygons to approximate pi, a concept that’s still relevant in math today!
Now, let’s talk about real-world applications! Understanding circles isn’t just about numbers; it influences various fields like architecture, engineering, and art. For example, when designing a wheel, engineers need to calculate both circumference and area to ensure proper functionality and aesthetics. Similarly, architects utilize these principles to create circular structures, making sure they are not only beautiful but also stable and practical. What a wonderful world where math meets creativity!

Related Questions

Latest Geometry Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy