Volume is a three-dimensional scalar quantity. If the radius of a cone is halved, but its height is doubled then the volume of the cone will become twice.
What is volume?
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a cone with radius of r units and the a height of h units is equal to,
Volume of the cone = (1/3) × π × r² × h
= (πr²h)/3
Now, if the radius of a cone is halved, but its height is doubled. Then the new volume of the cone will become,
Volume of the new cone = (1/3) × π × (r/2)² × 2h
= 2 × (πr²h)/3
Further, if the ratio of the volume of the cone before and the volume of the cone after is taken then the ratio will become.
Volume of the new cone / Volume of the cone = [2 × (πr²h)/3] / [(πr²h)/3]
Volume of the new cone = 2 × Volume of the cone
Hence, if the radius of a cone is halved, but its height is doubled then the volume of the cone will become twice.
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