To determine the formula for the volume of a right cone with base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex], let's carefully analyze each option provided.
A. [tex]\( V = \frac{1}{3} B h \)[/tex]
B. [tex]\( V = B h^2 \)[/tex]
C. [tex]\( V = 3 B h \)[/tex]
D. [tex]\( V = -\frac{1}{3} B h \)[/tex]
The standard formula for the volume of a right cone is derived from the fact that the volume of a cone is one-third the volume of a cylinder with the same base area and height. A cylinder with base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex] has a volume of [tex]\( B \times h \)[/tex]. Therefore, the volume [tex]\( V \)[/tex] of a right cone is given by:
[tex]\[ V = \frac{1}{3} B h \][/tex]
Among the four given options, Option A:
[tex]\[ V = \frac{1}{3} B h \][/tex]
is the correct formula for the volume of a right cone with base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex]. Thus, the formula for the volume of a right cone with base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex] is:
[tex]\[ V = \frac{1}{3} B h \][/tex]
Hence, the correct answer is:
A. [tex]\( V = \frac{1}{3} B h \)[/tex]
