Circle Problem

1-
A large circular pizza with an area of 289Ï€ inches is placed inside a square box that is just large enough to hold it. If the box is two inches deep, what is the volume of the box in cubic inches?

From the diagram:

Let radius of the pizza be r. So, side of the square box = 2r
We already know that the area of the pizza is 289*pi = pi*r*r
So, r^2 = 289. So r = 17

Volume of the box = Length of the box * Breath of the box * Height of the box
Length of the box = 2r = 2*17 = 34 inches
Breadth of the box = 2r = 2*17 = 34 inches
Height of the box = 2 inches
Volume of the box = 34*34*2 = 2312 cubic inches

The circumference of a circle with an area of 225π is divided into 60 identical arcs. What is the length of each arc, divided by π ?

The area of a circle with radius r = π*r*r = 225*π. So, radius^2 = 225 and radius (r) = 15
Circumference of the same circle = 2*Ï€*r = 2*Ï€*15 = 30*Ï€
If the circumference of the circle is divided into 60 identical arcs then length of each arc = 30*π/60 = π/2
length of each arc, divided by π = [spoiler](π/2)/π = 1/2[/spoiler]

The area of a circle with radius r = π*r*r = 81*π. So, radius^2 = 81 and radius (r) = 9
Circumference of the same circle = 2*Ï€*r = 2*Ï€*9 = 18*Ï€.

Since triangle DEF is an equilateral triangle. Length of arc DE = Length of arc EF = Length of arc FD
Length of arc DE + Length of arc EF + Length of arc FD = Circumference of the circle
3*Length of arc DE = Circumference of the circle
3*Length of arc DE = 18*Ï€
Length of arc DE = 6*Ï€
Length of arc DE, divided by π = (6*π)/π = 6