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A heap of wheat is in the form of a cone whose diameter is 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.

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.
 

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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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