Question

A heap of rice is in the form of a cone of diameter 9 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 that a heap of rice is in the form of a cone.

Height of a heap of rice (h) = 3.5 m

And diameter of a heap of rice = 9 m

∴ Radius of a heap of rice (r) = ${\displaystyle \frac{9}{2}}$ m  ...${\displaystyle [\because \text{Radius}=\frac{1}{2}\times \text{diameter}]}$

So, volume of rice = ${\displaystyle \frac{1}{3}\pi {\text{r}}^2\text{h}}$

= ${\displaystyle \frac{1}{3}\times \frac{22}{7}\times \frac{9}{2}\times \frac{9}{2}\times 3.5}$

= ${\displaystyle \frac{6237}{84}}$

= 74.25 m³

Now, canvas cloth required to just cover heap of rice

= Surface area of a heap of rice

= πrl

= ${\displaystyle \frac{22}{7}\times \text{r}\times \sqrt{{\text{r}}^2+{\text{h}}^2}}$

= ${\displaystyle \frac{22}{7}\times \frac{9}{2}\times \sqrt{{\left(\frac{9}{2}\right)}^2+{\left(3.5\right)}^2}}$

= ${\displaystyle \frac{11\times 9}{7}\times \sqrt{\frac{81}{4}+12.25}}$

= ${\displaystyle \frac{99}{7}\times \sqrt{\frac{130}{4}}}$

= ${\displaystyle \frac{99}{7}\times \sqrt{32.5}}$

= 14.142 × 5.7

= 80.61 m²

Hence, 80.61 m² canvas cloth is required to just cover the heap.