A container is made up of a hollow cone with an internal base radius of r cm and a hollow cylinder with the same base radius and an internal height of 4r cm. Given that the height of the cone is three-fifths of the height of the cylinder and 7 litres of water is needed to fill the conical part of the container completely, find the amount of water needed to fill the container completely, giving your answer in litres.
Answers
Given,
Radius of the base of cone = r centimetres
Radius of the base of cylinder = r centimetres
Height of the cylinder = 4r centimetres
Height of the cone = 3/5 × 4r = 12r/5 centimetres
Volume of cone = 7 litres = 7000 cm³
For, calculating the total volume of the container,we have to calculate the value of r³.
Now,
Volume of cone = 1/3 × π × (r)² × 12r/5 = 4πr³/5 cm³
Now,comparing the value of the volume of cone that we have calculated and the volume of cone that given in the question,we will get the following mathematical equation ;
4πr³/5 = 7000
r³ = 7000×5/4π
r³ = 35000/4π
So,
The volume of cylinder = π × r² × 4r = 4πr³ = 4π × 35000/4π = 35000 cm³
So,the total volume = 35000+7000 = 42000 cm³ = 42 litres
Hence,42 litres of water is needed to completely fill the container.
Answer:
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