A top is shaped like a cone surmounted by a hemisphere. The entire top

1.	A top is shaped like a cone surmounted by a hemisphere. The entire top is 5cm in height and the daimeter of hemisphere is 7 cm. Find the total surfacearea of the top
Answer» Given, the height of entire top = 5 cm and the diameter of top = 7 cm ∴ radius of hemisphere = 7/2 = 3.5 cm As both the hemisphere and cone are on the same base, therefore, radius of hemisphere = radius of cone = 3.5 cm Now the height of cone h = height of top – radius of hemisphere= (5 – 3.5) cm = 1.5 cm In order to calculate the total area of top, we have to find out the sum of curved surface area of both the cone and the hemisphere. ∴ Total Area = C.S.A of cone + C.S.A. of Hemisphere = πrl + 2πr^2 = πr(l + 2r) l = sqrt(r^2 + h^2) l = sqrt(3.53.5 + 1.51.5)l = sqrt(15.5)l = 3.93 Total Area = 22/7*3.5(3.93 + 7)= 11(10.93)= 120.93 cm^2

A top is shaped like a cone surmounted by a hemisphere. The entire top is 5cm in height and the daimeter of hemisphere is 7 cm. Find the total surfacearea of the top

Answer»

Given, the height of entire top = 5 cm and the diameter of top = 7 cm

∴ radius of hemisphere = 7/2 = 3.5 cm

As both the hemisphere and cone are on the same base, therefore,

radius of hemisphere = radius of cone = 3.5 cm

Now the height of cone h = height of top – radius of hemisphere= (5 – 3.5) cm = 1.5 cm

In order to calculate the total area of top, we have to find out the sum of curved surface area of both the cone and the hemisphere.

∴ Total Area = C.S.A of cone + C.S.A. of Hemisphere = πrl + 2πr^2 = πr(l + 2r)

l = sqrt(r^2 + h^2) l = sqrt(3.5*3.5 + 1.5*1.5)l = sqrt(15.5)l = 3.93

Total Area = 22/7*3.5(3.93 + 7)= 11(10.93)= 120.93 cm^2