Question

Dan Perkins goat is attached to the corner of the 14-foot-by-7-foot pump house by a 14-foot length of rope. The goat eats the grass around the pump house as shown in the diagram. This pattern consists of three-fourths of a circle of radius 14 feet and one-fourth of a circle of radius 7 feet. What area of grass can Dan Perkins goat eat? Use 3.14 as an approximate value

Answer 1

This pattern consists of three-fourths of a circle of radius 14 feet and one-fourth of a circle of radius 7 feet. What area of grass can Dan Perkins goat eat?

We know that the formula for the area of the pitch circle are:
$\pi*r^2*\alpha$ where alpha is the pinch of circle, r is radius, and pi is mathematics constant approximately equal 3,14

$\pi*14^2*\frac{3}{4}+\pi*7^2*\frac{1}{4}=461,58+38,465=500,045(feet^2)$