Question

What will total surface area of sphere when we cut it into four equal part?

Answer 1

When a sphere is cut into to equal halves, we get two hemispheres.
The volume of each hemisphere will be half of the volume of the sphere.
Volume of each hemisphere, V = ⅔πr³
The curved surface area of the hemisphere will also get halved.
CSA = 2 × area of circle = 2 πr²
TSA of hemisphere = CSA+Circular Area = 2 πr²+πr² = 3 πr²

The volume of each half will be half of the sphere's volume
Vol(sphere)=(4/3)πr^3
Vol(hemisphere)=(2/3) πr^3
The total surface area will be 2( surface Area of hemisphere)
surface Area of hemisphere =3πr^2
So the total surface area =6πr^2
Surface Area of Sphere = 4πr^2
Increase in surface =(6–4)πr^2 =2πr^2
% increase = (2πr^2/4πr^2) ×100
= 5 0 %
Hence the total volume remains the same and the surface area increases by 50%
Hope it helped!!!