a model of a solid structure in the shape of frustum of a cone with hemispherical top. The diameter of the hemispherical part is 70 cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 28 cm and slant height of 60 cm.)

Question

a model of a solid structure in the shape of frustum of a cone with hemispherical top. The diameter of the hemispherical part is 70 cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 28 cm and slant height of 60 cm.)
(a) The area of hemispherical surface.

b) The total surface area of the model

Steve · Accepted Answer

2/5 of the height of the cone is missing. The complete cone would have a slant height of 100.

The lateral area of a cone is πrs, so what we have is π(35)(100) - π(14)(40) = 2940π

The hemisphere has area 2πr^2 = 2π(35^2) = 2450π

The bottom of the shape is a circle of radius 14, with area 196π

So, add 'em all up for the total area.

lagat · Answer

the total surface area of the model