question_answer

A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the toy. \[\left( use\,\pi =\frac{22}{7} \right)\]

Answer:

Given, the base radius of cone, \[r=3.5\,cm\]

Total height of cone, \[(h+r)=15.5\text{ }cm\]

and base diameter of hemisphere \[=7\text{ }cm\]

Now, \[h=(15.5-3.5)\text{ }cm=12\text{ }cm\]

So, slant height,              \[l=\sqrt{{{h}^{2}}+{{r}^{2}}}=\sqrt{{{(12)}^{2}}+{{(3.5)}^{2}}}\]

\[=\sqrt{144+12.25}\]

\[=12.5\,cm\]

\[\therefore \] Total Surface Area \[=\pi rl+2\pi {{r}^{2}}\]

\[=\frac{22}{7}\times 3.5\times 12.5+2\times \frac{22}{7}\times 3.5\times 3.5\]

\[=\frac{22}{7}\times 3.5(12.5+2\times 3.5)\]

\[=11(19.5)\]

\[=214.5\,c{{m}^{2}}\]