Question

A builder has 100 m of fencing wire. He can use this wire to enclose a circular garden or a square garden. If he wants to maximize the enclosed area, what is the approximate ratio of the area of the largest possible circular garden to the area of the largest possible square garden, using the entire 100 m of wire?

• A. 1 : 1
• B. 1.27 : 1
• C. 1.57 : 1
• D. 2 : 1

Answer 1

Answer:

B. 1.27 : 1

Using the entire (100) m wire:

Circular garden

Circumference:

$2\pi r = 100$
$r = \frac{50}{\pi}$

Area of circle:

$\pi r^2$

$\pi \left(\frac{50}{\pi}\right)^2$

$\frac{2500}{\pi}$

Square garden

Perimeter:

4s = 100
s = 25

Area of square:

$25^2 = 625$

Ratio

$\frac{\text{Area of circle}}{\text{Area of square}}$

$\frac{2500/\pi}{625}$

$\frac{4}{\pi}$

Using $(\pi \approx 3.14)$:

$\frac{4}{3.14} \approx 1.27$

Therefore, the approximate ratio is:

$\boxed{1.27:1}$