Abigail is participating in a science fair where she has to create a model of a volcano. She decides to make the volcano in the shape of a cone. If the volume of the cone-shaped volcano model is the same as the options given below, which one should she choose?
To determine which option Abigail should choose for the volume of her cone-shaped volcano model, we need to compare the given options to the volume of a cone formula.
The volume of a cone is given by the formula: V = (1/3)πr^2h, where V is the volume, r is the radius of the base of the cone, and h is the height of the cone.
Let's examine the options given and compare them to the volume formula:
A) V = πr^3
This formula does not represent the volume of a cone. The exponent of 3 suggests the volume of a sphere, not a cone. This option is incorrect.
B) V = (2/3)πr^2h
This formula represents the volume of a cone in the correct format. The ratio of (2/3) scales the volume compared to the (1/3) ratio in the volume formula. Therefore, this option is incorrect.
C) V = (1/3)πr^2h
This formula represents the volume of a cone in the correct format. The (1/3) ratio matches the ratio in the volume formula. Therefore, this option is correct.
D) V = 3πr^2h
This formula is similar to the volume formula, but the missing ratio of (1/3) in front of πr^2 makes the proportion incorrect. This option is incorrect.
Therefore, Abigail should choose option C) V = (1/3)πr^2h as the volume for her cone-shaped volcano model.