There are 45 conical heaps of wheat, each of them having diameter 80 cm and height 30 cm. To store the wheat in a cylindrical container of the same radius, what will be the height of cylinder?
Answers
Dear student,
Answer: Height of cylinder would be : 450 cm or 4.5 m
Solution: As 45 conical heaps of wheat, each of them having diameter 80 cm and height 30 cm.
So,calculate the volume of 1 conical heap and multiply with 45,so as to volume of all 45 heap are to be calculate.
Volume of cone = 1/3 π r² h
as r = 40 cm, h = 30 cm ∴ radius = diameter/2
Volume of cone = 1/3 (3.14 )(40)²( 30)
Volume of cone = 50265.48 cm³
total volume of 45 conic heap of wheat: 45 × 50265.48 = 2,261,946.71 cm³
Volume of cylinder = π r² h
radius of cylinder r = 40 cm
since volume of both will be same; volume of 45 conic heap = volume of cylinder
π r² h = 2,261,946.71
h = 2,261,946.71/( π × 40 ×40)
h = 450 cm
Height of cylinder would be : 450 cm or 4.5 m.
Hope it helps you.