MATH SOLVE

2 months ago

Q:
# A sphere with radius 16 m is cut by a plane that is 9 m below its center. what is the best approximation of the area of the circle formed by the intersection of the plane and the sphere?

Accepted Solution

A:

the complete question in the attached figure

we know that

the equation of a sphere is

(x-h)²+(y-k)²+(z-l)²=r²

let's assume that the center of the sphere is at the origin

so

(h,k,l)-------> (0,0,0)

for r=16 m

(x-h)²+(y-k)²+(z-l)²=r²--------> (x)²+(y)²+(z)²=16²

for z=9 m

(x)²+(y)²+(9)²=16²--------> (x)²+(y)²=256-81--------> (x)²+(y)²=175

the radius of the circle is r=√175 m

so the area of the circle A=pi*r²-----> A=pi*175-----> A=549.5 m²

the answer is

the area of the circle is 549.5 m²

we know that

the equation of a sphere is

(x-h)²+(y-k)²+(z-l)²=r²

let's assume that the center of the sphere is at the origin

so

(h,k,l)-------> (0,0,0)

for r=16 m

(x-h)²+(y-k)²+(z-l)²=r²--------> (x)²+(y)²+(z)²=16²

for z=9 m

(x)²+(y)²+(9)²=16²--------> (x)²+(y)²=256-81--------> (x)²+(y)²=175

the radius of the circle is r=√175 m

so the area of the circle A=pi*r²-----> A=pi*175-----> A=549.5 m²

the answer is

the area of the circle is 549.5 m²