Question

A heap of rice is in the form of a cone of diameter $9m$ and height $3.5m$. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Answer 1

Step 1: Find the slant height

Diameter of the conical heap$=9cm$(radius is half of the diameter)

Radius of the conical heap$=\frac{9}{2}=4.5cm$

Now we will determine the slant height of the conical heap,

$$\begin{gathered} l=\sqrt{r^2+h^2} \\ \Rightarrow l=\sqrt{4.5^2+3.5^2} \\ \Rightarrow l=\sqrt{20.25+12.25} \\ \Rightarrow l=\sqrt{32.5} \\ \Rightarrow l=5.7cm \end{gathered}$$

Step 2: Find the volume of the rice

Volume of Rice $=$ Volume of cone

$=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

$=\frac{1}{3}\times \frac{22}{7}\times 4.5\times 4.5\times 3.5=74.25c{m}^3$

Thus, the volume of the rice$=74.25c{m}^3$

Step 3: Find the canvas requires

Canvas requires to just cover the conical heap$=$ Curved surface area of the conical heap

$=\mathrm{\pi rl}$

$=\frac{22}{7}\times 4.5\times 5.7=80.61{\mathrm{cm}}^2$

Hence, the canvas requires to just cover the conical heap$=80.61c{m}^2$.