Question

question 3 of 10
what is the formula for the volume of a right cone with base area b and height h?
a. ( v=\frac{1}{3}bh )
b. ( v = bh )
c. ( v=-\frac{1}{3}bh )
d. ( v = 2bh^{2} )

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is derived from the relationship with a cylinder. A cone with the same base area \( B \) and height \( h \) as a cylinder has a volume that is one - third of the cylinder's volume.

Step2: Cylinder volume formula

The volume formula of a cylinder is \( V = Bh \).

Step3: Cone volume formula

Since the cone's volume is one - third of the cylinder's volume (with the same base and height), the volume formula of a right cone is \( V=\frac{1}{3}Bh \).

Answer:

A. \( V=\frac{1}{3}Bh \)