Question

A toy is in the shape of a cylinder surmounted
by a hemisphere. The height of the toy is 25 cm.
Find the total surface area of the toy if its
common diameter is 12 cm.​

Answer 1

$\huge{\mathcal{\blue{\underline{Answer}}}}$

First , the height of the cylinder = Height of the toy - height of the hemisphere

= 25cm - 12cm

$\implies{\large{\blue{13cm}}}$

The curved surface area of the cylinder :

$= \pi \: r(h + r) \\ = \frac{22}{7} \times 12cm(13cm + 12cm) \\ = 942cm {}^{2}$

Now the curved surface area of the surmounted hemisphere :

$= 2\pi \: r {}^{2} \\ = 2 \times \frac{22}{7} \times 12cm \times 12cm \\ = 9 05cm {}^{2}$

✝ Total surface area of the toy = curved surface area of hemisphere + curved surface area of cylinder

$= 942cm {}^{2} + 905cm {}^{2} \\ = 1847cm {}^{2}$