Question

The total surface area of a solid hemisphere is 1848 sq. cm. A solid right circular cone is made by melting this hemisphere. If the radius of base of the cone is equal to the radius of the hemisphere , then what will be the height of the cone ?

Answer 1

Let the radius of the hemisphere be r cm
So , the total surface area of the hemisphere = ` 3 pir^(2) ` sq - cm
As per question , ` 3pir^(2) = 1848`
or , ` 3 xx 22/7 xx r^(2) or , r^(2) = (1848 xx 7) (3 xx 22 )`
or , `r^(2) = 196 or , r = 14`
Also , the volume of the hemisphere ` = 2/3 pi r^(3) ` cc
and the volume of the cone ` = 1/3 pir^(2) h` cc
As per question , ` 2/3 pir^(3) = 1/3 pir^(2) h`
` rArr h = (2pir^(3))/(pir^(2)) rArr h = 2r rArr h = 2r rArr h = 2 xx 14 rArr h = 28 `
Hence the height of the cone = 28 cm