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What is the formula for the volume of a right cone with base area [tex]\(B\)[/tex] and height [tex]\(h\)[/tex]?

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]

Sagot :

GinnyAnsweridn
To find the volume of a right cone with a base area [tex]\(B\)[/tex] and height [tex]\(h\)[/tex], we use the standard formula for the volume of a cone.

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. The formula for the volume [tex]\(V\)[/tex] of a right cone (a cone where the apex is directly above the center of the base) is derived as follows:

1. Formula for the volume of a cone:

[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

2. Substitute the given variables:
- Base Area = [tex]\( B \)[/tex]
- Height = [tex]\( h \)[/tex]

Thus, the formula for the volume of a right cone becomes:

[tex]\[ V = \frac{1}{3} B h \][/tex]

Therefore, the correct answer is:
A. [tex]\( V = \frac{1}{3} B h \)[/tex]
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