What is the formula for the volume of a right cone with base area $B$ and height $h$?
A. $V=\frac{1}{3} B h$
B. $V=-\frac{1}{3} B h$
C. $V=B h$
D. $V=2 B h^2$
Answer (1)
The problem requires identifying the correct formula for the volume of a cone.
The volume of a cone is given by V = 3 1 B h , where B is the base area and h is the height.
Comparing this with the given options, we find that option A matches the formula.
The correct answer is: V = 3 1 B h .
Explanation
Problem Analysis The question asks for the formula for the volume of a right cone with base area B and height h . We need to identify the correct formula from the given options.
Recall the Volume Formula The volume of a cone is given by the formula: V = 3 1 B h where B is the area of the base and h is the height of the cone.
Compare with Options Comparing the formula V = 3 1 B h with the given options: Option A: V = 3 1 B h - This matches the formula. Option B: V = − 3 1 B h - This is incorrect because volume cannot be negative. Option C: V = B h - This is the volume of a prism, not a cone. Option D: V = 2 B h 2 - This is incorrect and has the wrong dimensions.
Final Answer The correct formula for the volume of a right cone with base area B and height h is: V = 3 1 B h Therefore, the answer is option A.
Examples
Cones are common in everyday life, from ice cream cones to traffic cones. Knowing the volume of a cone is useful in many practical situations. For example, if you're filling ice cream cones at a shop, you'd want to know the volume to ensure you don't overfill them. Similarly, engineers use the volume formula to calculate the amount of material needed to construct conical structures or containers. The formula V = 3 1 B h allows for efficient and accurate calculations in these scenarios.
