question_answer

The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

Answer:

Slant height of frustum  \['l'=\text{ }4\text{ }cm\]

Perimeter of upper top \[=18\text{ }cm\]

\[\Rightarrow \]   \[2\pi R=18\,\,cm\Rightarrow R=\frac{9}{\pi }cm\]

Perimeter of lower bottom \[=6\text{ }cm\]

\[\Rightarrow \]   \[2\pi r=6\Rightarrow r=\frac{3}{\pi }cm\]

Curved S.A. of frustum \[=\pi l\left[ R+r \right]\]

\[=\pi \times 4\times \left[ \frac{9}{\pi }+\frac{3}{\pi } \right]\]

\[=\pi \times 4\times \frac{12}{\pi }=48\,\,c{{m}^{2}}\]