#### Questions

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use 𝜋 = 3.14).

Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm, supposing the material of which it is made weighs 10 grams per cubic cm.

#### Solution 1

Given diameter of cone 14cm

∴ Radius of cone=7cm

Height of cone =51cm

∴ Volume of cone=`1/3xxpir^2h`

`=1/3xx22/7xx7xx5xx51`

`= 2618 cm^3`

It is given that` 1cm^3` weight 10gm

`∴ 2618cm^3 weight (261xx10) gm `

i.e, 26.180kg.

#### Solution 2

To find the weight of the cone we first need to find its volume.

The formula of the volume of a cone with base radius ‘*r*’ and vertical height ‘*h*’ is given as

Volume of cone = `1/3 pi r^2h`

Here, the diameter is given as 14 cm. From this we get the base radius as *r* = 7 m.

Substituting the values of *r* = 7 cm and *h* = 51 cm in the above equation and using `pi=22/7`

Volume = `((22)(7)(7)(51))/((3)(7))`

= (22) (7) (17)

= 2618

Hence the volume of the given cone with the specified dimensions is 2618 m^{3}

Now, it is given that material of which the cone is made up of weighs 10 grams per cubic meter.

Hence the entire weight of the cone = (Volume of the cone) (10)

= (2618) (10)

= 26180 gram

Hence the weight of the cone is **26.18 kg**