• # question_answer A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 3. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the article. OR A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

 Given, Radius (r) of cylinder = Radius of hemisphere = 3.5 cm. Total SA of article = CSA of cylinder $+2\times$ CSA of hemisphere Height of cylinder, h = 10 cm TSA  $=\text{ }2\pi rh+2\times 2\pi {{r}^{2}}$ $=2\pi rh+4\pi {{r}^{2}}$ $=2\pi r\text{ (}h+2r)$ $=2\times \frac{22}{7}\times 3.5(10+2\times 3.5)$ $=2\times 22\times 0.5\times (10+7)$ $=2\times 11\times 17$ $=374\,\,c{{m}^{2}}$ OR Base diameter of cone = 24 m. $\therefore$ Radius $r=12\text{ }m$ Height of cone, $h=3.5\text{ }m$ Volume of rice in conical heap $=\frac{1}{3}\pi {{r}^{2}}h$ $=\frac{1}{3}\times \frac{22}{7}\times 12\times 12\times 3.5$ $=528\,{{m}^{3}}$ Now, slant height, $l=\sqrt{{{h}^{2}}+{{r}^{2}}}$ $=\sqrt{{{(3.5)}^{2}}+{{(12)}^{2}}}$ $=\sqrt{12.25+144}$ $=\sqrt{156.25}$ $=12.5\,m$ Canvas cloth required to just cover the heap = CSA of conical heap $=\pi rl$ $=\frac{22}{7}\times 12\times 12.5$ $=\frac{3300}{7}{{m}^{2}}$ $471.43\,\,{{m}^{2}}$.