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.
Given diameter of cone 14cm
∴ Radius of cone=7cm
Height of cone =51cm
∴ Volume of cone=`1/3xxpir^2h`
`= 2618 cm^3`
It is given that` 1cm^3` weight 10gm
`∴ 2618cm^3 weight (261xx10) gm `
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)
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