Cones a and b have the same height but different radii. If the volume of the cone a is 641.08 find the volume of cone b.

Question

Radius a is 7cm and radius b is 3.5cm.  

Answer 1

Let's find the cones' heights by solving for h in Cone A's volume equation:

 

V_A = (1/3)πr²h

641.08 = (1/3)π(7)²h

641.08 = (49/3)πh

39.25 = πh

12.49 = h

 

The cones' heights are both 12.49 cm.

 

 

Now you can solve for the volume of Cone B:

 

V_B = (1/3)πr²h

V_B = (1/3)π(3.5)²(12.49)

V_B = 4.16(3.5)²π

V_B = 51π

V_B = 160.22

 

The volume of Cone B is 160.22 cm³.