A toy is in the form of a cone surmounted on | vedclass

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(C) Given: Radius of hemisphere $(r)$ = $3.5\, cm = \frac{7}{2}\, cm$. Total height of the toy = $15.5\, cm$. Height of the cone $(h)$ = Total height

Vedclass · Accepted Answer

$214.5$

Vedclass · Answer

(C) Given: Radius of hemisphere $(r)$ = $3.5\, cm = \frac{7}{2}\, cm$. Total height of the toy = $15.5\, cm$. Height of the cone $(h)$ = Total height - Radius of hemisphere = $15.5 - 3.5 = 12\, cm$. Slant height of the cone $(l)$ = $\sqrt{r^2 + h^2} = \sqrt{(3.5)^2 + 12^2} = \sqrt{12.25 + 144} = \sqrt{156.25} = 12.5\, cm$. Total surface area of the toy = Curved surface area of cone + Curved surface area of hemisphere. $= \pi rl + 2\pi r^2 = \pi r(l + 2r)$. $= \frac{22}{7} 	imes 3.5 	imes (12.5 + 2 	imes 3.5) = 11 	imes (12.5 + 7) = 11 	imes 19.5 = 214.5\, cm^2$.

$A$ toy is in the form of a cone surmounted on a hemisphere. The radius of the cone as well as the hemisphere is $3.5\, cm$ and the total height of the toy is $15.5\, cm$. Find its total surface area (in $cm^2$).

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