Q : 9    A heap of wheat is in the form of a cone whose diameter is \small 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
 

Answers (1)

Given,

Height of the conical heap =  h = 3\ m

Base radius of the cone = r = \frac{10.5}{2}\ m

We know,

 The volume of a cone = \frac{1}{3}\pi r^2 h

The required volume of the cone formed = \frac{1}{3}\times\frac{22}{7}\times\left (\frac{10.5}{2} \right )^2\times3

\\ = 22\times\frac{1.5\times10.5}{4} \\ = 86.625\ m^3

Now,

The slant height of the cone = l = \sqrt{r^2+h^2}

\\ \Rightarrow l = \sqrt{3^2+5.25^2} = \sqrt{9+27.5625} \approx 6.05

We know, the curved surface area of a cone = \pi r l

The required area of the canvas to cover the heap  = \frac{22}{7}\times\frac{10.5}{2}\times6.05

= 99.825\ m^2

 

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