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प्रश्न
The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.
उत्तर
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^2 h`
It is given that the height of the cone is ‘h’ = 3.5 cm and that the volume of the cone is 3.3 liters
We know that,
1 liter = 1000 cubic centimeter
Hence, the volume of the cone in cubic centimeter is ` 3300 cm^3`.
We can now find the radius of base ‘r’ by using the formula for the volume of a cone, while using `pi = 22/7`
`r^2 = (3("Volume of the cone"))/(pih)`
= `((3)(3300)(7))/((22)(3.5))`
`r^2` = 900
r = 30
Hence the radius of the base of the cone with given dimensions is ‘r’ = 30 cm.
The diameter of base is twice the radius of the base.
Hence the diameter of the base of the cone is 60 cm
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