Question

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 total surface area of 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 ?

Answer 1

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