Question

Rahamal got a playing top (lattu) as his birthday presentation, which surprisingly had no colour on it. So he wanted to colour it with his crayons. The top is shaped like a cone surprisingly by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour.

Answer 1

Correct Answer - 39.6 sq-cm ( approx)
Total surface area of the top = curved surface area of the hemisphere + curved surface area of the cone.
Now, the curved surface area of the hemisphere `=1/2 xx 4 pi r^(2) = 2 pi r^(2) = (2xx(22)/(7)xx(3.5)/(2)xx(3.5)/(2))`sq-cm
Also, the height of the cone = height of the top - height ( radius) of the hemispherical part.
`=(5-(3.5)/(2)) cm = 3.25`cm.
So the slant height of the cone `=sqrt((3.5/2)^(2)+(3.25)^(2))cm=3.7cm` (approx)
`:.` curved surface area of cone `=((22)/(7)xx(3.5)/(2)xx3.7)`sq-cm [ Formula `: pi r l` ]
Hence the total surface area of the top
`=(2xx(22)/(7)xx(3.5)/(2)xx(3.5)/(2)) sq-cm + ((22)/(7)xx(3.5)/(2)xx3.7)sq-cm.=39.6 sq-cm `[(approx.)]