Question
EXERCISE 3
- 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.
- 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.
a) Find the values of
calculate
b) Round off
decimal places).
c) Compare the values of
the accuracy of your answers.
If
a)
decimal places).
b)
c) Compare the values of
accuracy of your answers.
Ask by Fleming Pollard. in South Africa
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Exercise 3 Solutions:
-
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.
- a)
-
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.
- a) Radius
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

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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!