The shape of the lower part of a solid object is like a hemisphere and the upper part like a right circular cone . If the surface area of the two parts be equal , then find the ratio of the length of radius and height of the cone .

Explanation

Let the radius of the hemisphere = r unit
` :.` the radius of the cone = r unit
Let the height of the cone = h unit
As per question
`2 pir^(2) = prrl ,` where l = slant height of the cone
` rArr 2r = l rArr 2r = sqrt(h^(2) + r^(2))`
`rArr 4r^(2) = h^(2) + r^(2) rArr 3r^(2) = h^(2)`
` rArr sqrt(3r) = h rArr r/h = 1/(sqrt(3)) rArr r : h = 1 : sqrt(3)`
Hence the required ratio = `1 : sqrt(3)`