question_answer

From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.

Answer:

Given, height of cylinder  \['h'=2.4\text{ }cm\]

Radius of base \['r\text{  }\!\!'\!\!\text{ }=0.7\text{ }cm\]

And slant height; \[l=\sqrt{{{h}^{2}}+{{r}^{2}}}\]

\[=\sqrt{{{(2.4)}^{2}}+{{(0.7)}^{2}}}\]

\[=\sqrt{6.25}\]

\[=2.5\,\,cm\]

Total surface area of the remaining solid

= CSA of cylinder + CSA of cone + Area of top

\[=2\pi rh+\pi rl+\pi {{r}^{2}}\]

\[=\pi r[2h+l+r]\]

\[=\frac{22}{7}\times 0.7[2\times 2.4+2.5+0.7]\]

\[=2.2[4.8+2.5+0.7]\]

\[=2.2\times 8=17.6\,\,c{{m}^{2}}\]