The cylinder has a volume of 30 cubic units. the cone and cylinder have the same height and the same base. what is the volume of the cone?

The volume of the cone is 10 units^3

Step-by-step explanation:

step 1

Find the equation of the volume of the cylinder

we know that

The volume of a cylinder is equal to

Vcylinder=pi r^{2} h

In this problem

Vcylinder=30 units^3

so

30=pi r^{2} h> equation A

step 2

Find the volume of the cone

we know that

The volume of the cone is equal to

Vcone=(1/3)pi r^{2} h > equation B

substitute equation A in equation B

Vcone=(1/3)(Vcylinder)

Vcone=(1/3)(30)

Vcone=10 units^3

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.