Quality Learning Support For Better Outcomes
First time here? Checkout the FAQs!
MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike

A wire, 4 meters long, is cut into two pieces. One is bent into a shape pf a square and the other into a shape of a circle.

  1. If the length of wire used to make the circle is x metres, write in terms of $x$ the length of the sides of the square in metres.
  2. Show the sum of the areas of the circle and the square is given by $f(x) = (\frac{1}{16} + \frac{1}{4\pi})x^{2} - \frac{x}{2} + 1$
  3. How should the wire be cut so that the sum of the areas of the circle and the square is a minimum?
in Mathematics by Diamond (78,454 points) | 254 views

1 Answer

1 like 0 dislike
Best answer
1. $= \dfrac{4-x}{4} $m

2. Area of square $=(\dfrac{4-x}{4})^2$

  Area of circle $= \pi. r^2$

but circumference $= \pi.d$

                    $x= \pi.d$

                   $d= \dfrac{x}{\pi}$

                $ r= \dfrac{x}{2}.\pi$

$A = \dfrac{(\pi.x^2)}{4}\pi^2 = \dfrac{x^2}{4\pi}$

   adding 2 areas= $\dfrac{x^2}{4\pi }+ [\dfrac{(4-x)}{4}]^2 $

$= (\dfrac{1}{16} + \dfrac{1}{4\pi}).x^2 - \dfrac{x}{2} + 1$

3. $\dfrac{dA}{dx} = 2.x.(\dfrac{1}{16} + \dfrac{1}{4\pi}) - \dfrac{1}{2} = 0$

, solving $x= 3.52$m for circle and $4-3.52= 0.48$m for square
by Diamond (44,036 points)
selected by

Related questions

0 like 0 dislike
1 answer

Join the MathsGee community and get study support for success - MathsGee provides answers to subject-specific educational questions for improved outcomes.

On MathsGee Answers, you can:

1. Ask questions
2. Answer questions
3. Comment on Answers
4. Vote on Questions and Answers
5. Donate to your favourite users

Enter your email address:

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

MathsGee ZOOM | eBook