A solid metallic object is shaped like a double cone the radius of the base of both cone is same but the height are different if this phone is immersed in water find the quantity of water it will displace
Answers
The quantity of water displaced by the double cone on being immersed in it is (πr²/3) × (h + h') cubic units.
• A double cone, as the name suggests, is made up of two cones. The figure has been attached below for better understanding.
• Given,
Radius of the base of both the cones is same, but heights are different.
Let r be the radius of both the cones.
Let the height of one cone be h and the height of the other cone be h'.
• The double cone on being immersed in water replaces water equal to the total volume of the cones
• Volume of a cone = πr²h / 3
where r is the radius of the base of the cone, and h is the height of the cone.
Therefore, volume of the first cone = πr²h / 3 cubic units
Volume of the second cone = πr²h' / 3 cubic units
Therefore, total volume of the double cone (V) = Volume of cone 1 + Volume of cone 2
=> V = (πr²h / 3) + (πr²h' / 3) cubic units
=> V = (πr²/3) × (h + h') cubic units [taking out πr²/3 as the common term]
• Thus, the volume of water displaced by the double cone is (πr²/3) × (h + h') cubic units.
