A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical par are 13cm and 5cm respectively. The radii of the hemispherical and conical parts re the same as that of the cylindrical part. Calculate the surface area of the toy if height of the conical part is 12 cm.

Explanation

Let `{r} {} {cm}` be the radius and `{h} {cm}` the height of the cylindrical part. Then, `{r}=` `5 {~cm}, {~h}=13 {~cm}`


Clearly radii of the spherical part and base of the conical part are also `{rcm}`. Let `{h}_{1} {~cm}` be the height, `1 {~cm}` be the slant height of the conical part.

Then



`{l}^{2}={r}^{2}+{h}_{1}^{2} \Rightarrow {l}=\sqrt{{r}^{2}+{h}_{1}^{2}} \Rightarrow {l}=\sqrt{5^{2}+12^{2}}=13 {~cm}`


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