Area of Circle

[phoenix9801]

1-
A circle is divided into identical sectors. Each sector has a central angle of 15° and an area of 13π. What is the area of the circle, divided by π ?

2-
A walker travels the circumference of a circular reservoir with an area of 81π square miles in 12 minutes. Moving at twice the speed of the walker, a runner travels the circumference of a different circular reservoir in 10 minutes. What is the area (in square miles) of the second reservoir, divided by π ?

[neelgandham]

A circle is divided into identical sectors. Each sector has a central angle of 15° and an area of 13π. What is the area of the circle, divided by π ?

Angle of the sector = 15°
Total angle of the circle = 360°
Total number of sectors = Total angle of the circle /Angle of the sector = 360°/15° = 24
Area of a sector = 13Ï€
Area of the circle = Area of 24 sectors = 24*13Ï€ square units.
Area of the circle, divided by π = 24*13π/π = 24*13 = 312

[neelgandham]

A walker travels the circumference of a circular reservoir with an area of 81π square miles in 12 minutes. Moving at twice the speed of the walker, a runner travels the circumference of a different circular reservoir in 10 minutes. What is the area (in square miles) of the second reservoir, divided by π ?

Area of the circular reservoir of radius r = 81π = π*r*r. i.e. r = 9 miles
Circumference of the circular reservoir of radius r = 2*Ï€*r = 2*Ï€*9 = 18*Ï€ miles.
Speed of the walker = Distance/Time = 18*Ï€ /12 = 1.5*Ï€ miles per minute.

Speed of the walker on the second reservoir = 2* 1.5*Ï€ = 3*Ï€ miles per minute.
Time taken to walk around the reservoir = 10 minutes
Total distance walked = Circumference of the second circular reservoir = Speed * Time = 3*Ï€*10 = 30*Ï€
Miles.
Circumference of the second circular reservoir (of radius say R) = 2*Ï€*R = 30*Ï€. i.e. R = 15miles
Area (in square miles) of the second reservoir, divided by π = (π*R*R)/π = R*R = 15*15 = 225