Question

A plane cuts a sphere 10 meters above from the center of the sphere as shown in the figure. Compute the surface area of the sphere before and after a zone is cut off the sphere

 

Area of sphere before zone is cut off = _______ m^2

Area of sphere after the zone is cut off = __________ m^2

Answer 1

A plane cuts a sphere 10 meters above from the center of the sphere as shown in the figure. Compute the surface area of the sphere before and after a zone is cut off the sphere.

Area before cutting is A1 = 4πR^2
Where R = 15, hence A1 = 900π

Area after cutting is A2 = A1 – Area of cap + Area of circular surface (the cut plane)
Area of cap = A3 = 2πRh,
Where h = h1 = R – 10 = 15 – 10 = 5 m.
Hence, A3 = 2π*15*5 = 150π/3

Area of circular surface is A4 = πa^2,
Where a = sqrt(15^2 – 10^2) = sqrt(125)
Hence, A4 = πa^2 = 125π

Finally, A2 = A1 – A3 + A4
A2 = 900π - 150π/3 + 125π
A2 = (π/3)(2700 – 150 + 375)

A2 = 2925π/3

Comments

Used a wrong formula earlier. Correctef now.