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) = `9/2` m  ...`[∵ "Radius" = 1/2 xx "diameter"]`

So, volume of rice = `1/3π"r"^2"h"`

= `1/3 xx 22/7 xx 9/2 xx 9/2 xx 3.5`

= `6237/84`

= 74.25 m³

Now, canvas cloth required to just cover heap of rice

= Surface area of a heap of rice

= πrl

= `22/7 xx "r" xx sqrt("r"^2 + "h"^2)`

= `22/7 xx 9/2 xx sqrt((9/2)^2 + (3.5)^2)`

= `(11 xx 9)/7 xx sqrt(81/4 + 12.25)`

= `99/7 xx sqrt(130/4)`

= `99/7 xx sqrt(32.5)`

= 14.142 × 5.7

= 80.61 m²

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