Question

Kajal got a playing top (lattu) as her birthday gift, which surprisingly had no colour on it. She wanted to colour it with her crayons. The top is shaped like a cone, surmounted by a hemisphere. The entire top is $5	ext{ cm}$ in height and the diameter of the top is $3.5	ext{ cm}$. Find the area she has to colour. [Use $\pi = \frac{22}{7}$]

Accepted Answer

Radius $r = \frac{3.5}{2} = 1.75	ext{ cm} = \frac{7}{4}	ext{ cm}$. Height of hemispherical part $= r = 1.75	ext{ cm}$. Height of conical part $h = 5 - 1.75 = 3.25	ext{ cm} = \frac{13}{4}	ext{ cm}$. Slant height of cone $l = \sqrt{r^2 + h^2} = \sqrt{(1.75)^2 + (3.25)^2} = \sqrt{3.0625 + 10.5625} = \sqrt{13.625} \approx 3.7	ext{ cm}$. Area to colour $= 	ext{CSA of hemisphere} + 	ext{CSA of cone}$ $$= 2\pi r^2 + \pi r l = \pi r (2r + l)$$ $$= \frac{22}{7} 	imes 1.75 	imes (2(1.75) + 3.7) = 5.5 	imes (3.5 + 3.7) = 5.5 	imes 7.2 = 39.6	ext{ cm}^2$$

Surface area of a playing top (lattu)

Explanation

Practise this under board exam conditions