Question

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.

Answer 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.  

Answer 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 m³

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