Question

If the radius of a solid sphere be decreased by 1 cm, then the curved surface area of it is decreased by 88 sq-cm. What was the radius of the square?

Answer 1

Let the radius of the solid sphere be r cm .
`:.` the curved surface area of the sphere `=4pir^(2)` sq-cm.
Now, if the radius of the sphere is decreased by 1 cm, then the curved surface of it will be `4pi(r-1)^(2)` sq-cm.
As per question , `4pir^(2)-4pi(r-1)^(2)`=88
or, `4pi[r^(2)-(r-1)^(2)]`=88
or, `4xx(22)/(7)[(r+r-r)]=88 "or" 4xx(22)/(7)[(2r-1)]=88`
or, `2r-1=(88xx7)/(4xx22)` or,2r-1=7 or, 2r=8 or, r=4.
Hence the radius of the solid sphere was 4 cm.