A toy is in the shape of a right circular cylinder with a hemisphere on one end and a come on the other. The radius and height of the cylindrical pan are $5 c m$ and $13 c m$ respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is $30 c m$ .

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Solution

Perimeter is the sum of the length of boundary of any shape
$H = 30 c m h = 13 c m$
$r = 5 c m$
$h_{c} = H - h - r$
$= 30 - 13 - 5 = 12 c m$
SA of toy $= C S A$ of cone $+ C S A$ of cylinder $+ C S A$ of hemisphere
$= π r l + 2 π r h + 2 π r^{2}$
$= π r \sqrt{r^{2} + h^{2}} + 2 π r (h + r)$
$= π [5 (13) + 2 (5) (18)]$
$= 245 π$
$= 769.69 c m^{2}$

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A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm, respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.

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Perimeter is the sum of the length of boundary of any shape H=30 cmh=13 cmr=5 cmhc=H−h−r=30−13−5=12 cmSA of toy =CSA of cone +CSA of cylinder +CSA of hemisphere =πrl+2πrh+2πr2 =πr√r2+h2+2πr(h+r) =π[5(13)+2(5)(18)] =245π =769.69 cm2