Question

If the radius if a sphere is decreased by `(1)/(2)` times, then the curved surface area of the sphere will be changed by
A. `(1)/(2)` times
B. `(1)/(4)` times
C. `(1)/(8)` times
D. `(1)/(16)` times

Answer 1

If the radius of a sphere be r units, the curved surface area of it will be =S= `4pir^(2)` sq-units.
If the radius is decreased by `(1)/(2)` times, then the curved surface area
`=4pixx((r)/(2))^(2) "sq-units" =pir^(2) "sq-unit"=(1)/(4)xx4pir^(2) "sq-unit"=(1)/(4)xx "S sq-unte" =(S)/(4) "sq-units"`
`therefore` the new curved surface area of the sphere will be `(1)/(4)` times of the previous curved surface area.