The base of a cone has a radius of 4 millimeters and the height of the cone is 24 millimeters. What is the volume of the cone?

Question 6 options:

A. 32π mm3

B. 96π mm3

C. 128π mm3

D. 384π mm3

The volume of the cone is 128π mm³ ⇒ answer (C)

Step-by-step explanation:

* Lets study the cone

- Its base is a circle

- Its height the perpendicular distance from its vertex to

the center of the base

- The length of its slant height = √ (h² + r²)

- The volume of the con is 1/3 the volume of the cylinder

∵ The volume of the cylinder = πr²h

∴ The volume of the cone = (1/3) πr²h

* In our problem:

- r = 4 mm

- h = 24 mm

∴ Its volume = (1/3) * π * (4) ² * 24 = 128π mm³

* The volume of the cone is 128π mm³