Question
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?
Answers
GPT 3.5
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.
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.