Question

a cone surmounted on a hemisphere of same radii. if the surface area of a cone and hemisphere are equal find the ratio of the radius and height of the conical part

Answer 1

Answer:

given, SA is same. So,

πrl = 2πr² (pi gets cancelled)

r√h²-r² = 2r² (r gets cancelled)

√h²-r² = 2r

h²-r² = (2r)²

h²-r = 4r²

h² = 5r²

h²/r² = 5 (power 2 gets cancelled)

h/r = 5

h:r = 5

Step-by-step explanation:

πrl is the formula of CSA of cone, as is 2πr² of hemisphere.

l (slant height) can be written as √h²-r²