Question

A hole of radius r is bored through the center of a sphere of radius R>r. Find the volume of remaining portion of the sphere.

Answer 1

4/3*pi*R^2-4/3*pi*r^2

Answer 2

doesnt have any integral ?

Answer 3

didn't even think about that. DERP xD
2π ∫[0,√(R² - r²)] ((√(R² - x²))² - r²) dx
2π ∫ (R² - r² - x²) dx
2π((R² - r²)x - (x³/3))|[0, √(R² - r²)]
2π((R² - r²)^(3/2) - (1/3)(R² - r²)^(3/2) - 0)
(4π/3)(R² - r²)^(3/2)

Answer 4

such a noob

Answer 5

wait im so confused abiut the setting up of integral :(