Simple Math Question?

Question

If you have 48 ft of wire, how do you figure what shape produces the largest area with that given amount of wire?

Answer 1

A circle will enclose the largest area.  Nature understands this too which is why soap bubbles are spherical.

If you think about it, a circle will maximize the amount of area while minimizing the perimeter (or in this case circumference).

If you are unsure, try computing the area of a circle with circumference 48 ft.  Then compare that to a square with sides of 12 ft each (144 sq. ft.).  Try other shapes too.  The circle will win.

Circle, with circumference 48 ft.

C = 2 π r

48 = 2π r

r = 48/2π

r = 24/π

Area = π r²

Area = π(24/π)²

Area = 24²/π

Area = 183.3 sq. ft.

Answer 2

circle

area = pi*r*r = 48

Answer 3

I know a circle will give you a maximum area...but i'm not sure why

EQ> 1 : use pi r^2

first compute radius of circle using: 2*pi*r and solve for r then plug into eq. 1

Answer 4

It's a circle right?

Pie R ^2

Answer 5

If I have one jug that can hold 7 liters and I half fill it, and another jug that can hold 4 liters and fill that one to the top, how many jugs do I have?

Answer 6

The largest area is a circle with a diameter of 15.258 ft, giving an area of 182 square feet. A square of 12 by 12 ft would give you an are of 144 ft2