Answer:(i) 84 cm.
(ii) 5635π cm^2
Step-by-step explanation:
(i)
The volume of the cone = 1/3 π r^2 h
= 1/3 π 35^2 h.
The volume of the hemisphere = 2/3 π 35^3.
As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:
1/3 π 35^2 h = 2/3 π 35^3 * 6/5
h = 2/3 π 35^3 * 6/5 / 1/3 π 35^2
h = 84 cm (answer).
(ii) Surface area of the hemisphere = 2 π * 35^2 = 2450π cm^2.
Surface area of the cone = π r l where l = slant height.
l = √(35^2 + 84^2) = 91 cm.
So the surface area of the cone = 35*91 π = 3185π.
So the total surface area of the solid is 3185π + 2450π
= 5635π cm^2.
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