Solution:
perimeter of square =4x
perimeter of circle=2 pi r
then 4x+2 pi r=80
r=(40-2x)/pi
Area of square=
Area of circle=
Total area A=
A=
A=
A=
A=
Hello everyone.
Wish i could answer this question on my own,
The question is from october november 2008 AS level maths paper 1 exam paper
Question:
A wire, 80cm long is cut into two pieces. One piece is bent to form a square of side x cm and the other piece is bent to form a circle of radius r cm The total area of the square and circle is A cm^2
(i) show that A=
(pi+4)x^2 - 160x + 1600
-----------------------------
pi
I have no idea how to show that...
then the second question is just as difficult.
(ii) Given that x and r can vary, find the value of x for which A has a stationary value.
Would really love some help
Thanks
Peder
Hello, Peder!
A wire 80cm long is cut into two pieces.
One piece is bent to form a square of side cm
and the other piece is bent to form a circle of radius cm.
The total area of the square and circle is cm³.
(i) Show that: .
slovakiamath gave an excellent derivation.
(ii) Given that and can vary,
find the value of for which has a stationary value.
Differentiate , equate to zero, and solve for