QuestionWhich statement about cones is false? A. Cone has a circular base. B. Slant height is from vertex to base edge. C. Oblique cone's axis isn't perpendicular. D. Cone's volume is half that of a sphere with same radius and height. E. None are false.

Studdy Solution

STEP 1

Assumptions1. We understand the definition and properties of a cone. . We know the formula for the volume of a cone and a sphere.

STEP 2

Let's analyze each statement one by one.
Statement A A cone is a lot like a pyramid, except that it has a circular base.
This statement is true. A cone is similar to a pyramid but instead of a polygonal base, a cone has a circular base.

STEP 3

Statement B The slant height of a cone is the length from the vertex down to the edge of the circular base.
This statement is also true. The slant height of a cone is indeed the length from the vertex (the tip of the cone) to the edge of the circular base.

STEP 4

Statement C An oblique cone is a cone whose axis is not perpendicular to the circular base.
This statement is true as well. An oblique cone is defined as a cone with an axis that is not perpendicular to its base.

STEP 5

Statement D The volume of a cone is one-half the volume of a sphere with the same radius and height.
We need to verify this statement using the formulas for the volumes of a cone and a sphere.The volume $V$ of a cone is given by the formula $V_{cone} = \frac{1}{3}\pi r^2h$ where $r$ is the radius of the base and $h$ is the height of the cone.
The volume $V$ of a sphere is given by the formula $V_{sphere} = \frac{4}{3}\pi r^3$ where $r$ is the radius of the sphere.

STEP 6

Now, let's compare the volume of a cone to half the volume of a sphere with the same radius and height.
$\frac{1}{2}V_{sphere} = \frac{1}{2} \times \frac{4}{3}\pi r^3 = \frac{2}{3}\pi r^3$ This is not equal to the volume of a cone, which is $\frac{1}{3}\pi r^2h$ .Therefore, Statement D is false.

STEP 7

Statement None of these are false.
Since Statement D is false, Statement is also false.
The false statement is D The volume of a cone is one-half the volume of a sphere with the same radius and height.

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QuestionWhich statement about cones is false? A. Cone has a circular base. B. Slant height is from vertex to base edge. C. Oblique cone's axis isn't perpendicular. D. Cone's volume is half that of a sphere with same radius and height. E. None are false.

Studdy Solution

STEP 1

Assumptions1. We understand the definition and properties of a cone. . We know the formula for the volume of a cone and a sphere.

STEP 2

Let's analyze each statement one by one.
Statement A A cone is a lot like a pyramid, except that it has a circular base.
This statement is true. A cone is similar to a pyramid but instead of a polygonal base, a cone has a circular base.

STEP 3

Statement B The slant height of a cone is the length from the vertex down to the edge of the circular base.
This statement is also true. The slant height of a cone is indeed the length from the vertex (the tip of the cone) to the edge of the circular base.

STEP 4

Statement C An oblique cone is a cone whose axis is not perpendicular to the circular base.
This statement is true as well. An oblique cone is defined as a cone with an axis that is not perpendicular to its base.

STEP 5

STEP 6

Now, let's compare the volume of a cone to half the volume of a sphere with the same radius and height.
$\frac{1}{2}V_{sphere} = \frac{1}{2} \times \frac{4}{3}\pi r^3 = \frac{2}{3}\pi r^3$ This is not equal to the volume of a cone, which is $\frac{1}{3}\pi r^2h$ .Therefore, Statement D is false.

STEP 7

Statement None of these are false.
Since Statement D is false, Statement is also false.
The false statement is D The volume of a cone is one-half the volume of a sphere with the same radius and height.

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QuestionWhich statement about cones is false? A. Cone has a circular base. B. Slant height is from vertex to base edge. C. Oblique cone's axis isn't perpendicular. D. Cone's volume is half that of a sphere with same radius and height. E. None are false.

Studdy Solution

STEP 1

Assumptions1. We understand the definition and properties of a cone. . We know the formula for the volume of a cone and a sphere.

STEP 2

Let's analyze each statement one by one.Statement A A cone is a lot like a pyramid, except that it has a circular base.This statement is true. A cone is similar to a pyramid but instead of a polygonal base, a cone has a circular base.

STEP 3

Statement B The slant height of a cone is the length from the vertex down to the edge of the circular base.This statement is also true. The slant height of a cone is indeed the length from the vertex (the tip of the cone) to the edge of the circular base.

STEP 4

Statement C An oblique cone is a cone whose axis is not perpendicular to the circular base.This statement is true as well. An oblique cone is defined as a cone with an axis that is not perpendicular to its base.

STEP 5

STEP 6

STEP 7

Statement None of these are false.Since Statement D is false, Statement is also false.The false statement is D The volume of a cone is one-half the volume of a sphere with the same radius and height.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Let's analyze each statement one by one.
Statement A A cone is a lot like a pyramid, except that it has a circular base.
This statement is true. A cone is similar to a pyramid but instead of a polygonal base, a cone has a circular base.

Statement B The slant height of a cone is the length from the vertex down to the edge of the circular base.
This statement is also true. The slant height of a cone is indeed the length from the vertex (the tip of the cone) to the edge of the circular base.

Statement C An oblique cone is a cone whose axis is not perpendicular to the circular base.
This statement is true as well. An oblique cone is defined as a cone with an axis that is not perpendicular to its base.

Statement None of these are false.
Since Statement D is false, Statement is also false.
The false statement is D The volume of a cone is one-half the volume of a sphere with the same radius and height.