Question

a cylinder has a volume of 321 cubic units. if a cone has the same height and radius as the cylinder, what is its volume in cubic units​

Answer 1

1. First, let us write out the formula for the volume of a cylinder:

V = πr^(2)h

Now, given that the cylinder has a volume of 321 cubic units, we can rewrite the above formula with this new information:

321 = πr^(2)h

2. The volume of a cone is given by the following formula:

V = (1/3)πr^(2)h

Now, we can substitute 321 = πr^(2)h into the formula above to find the volume of the cone (this will work as the cone and cylinder have the exact same radius and height). Thus we get:

V = (1/3)πr^(2)h

V = (1/3)*321

= 107 cubic units

Note that there is another method that is perhaps more intuitive and can be used quite effectively in multiple choice questions, where working isn't required. What you should notice from the general formulas for the volume of a cone and a cylinder is that the volume of a cone is actually 1/3 of the volume of a cylinder (given that they have the same radius and height). Thus, if we know that the cone in our situation has the exact same radius and height as the cylinder, we can use this method as such:

Volume of cone = (1/3)*Volume of cylinder

Volume of cone = (1/3)*321

= 107 cubic units