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Flashcards: Apply the Revolving Disc Method and Washer Method

What is the disc method?

Finding the volume of a sphere

Finding the volume of a solid by finding the surface area and adding all surface areas of the solid

Finding the volume of a solid by taking a cross sectional of it and calculating the volume by adding infinitely many of these cross sections

Finding the area of a circle

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Flashcards: Apply the Revolving Disc Method and Washer Method

What is the disc method?

Finding the volume of a sphere

Finding the volume of a solid by finding the surface area and adding all surface areas of the solid

Finding the volume of a solid by taking a cross sectional of it and calculating the volume by adding infinitely many of these cross sections

Finding the area of a circle

Report an Error Copyright Notice

Flashcards: Apply the Revolving Disc Method and Washer Method

What is the disc method?

Your answer:

Finding the volume of a sphere

Your answer:

Finding the volume of a solid by finding the surface area and adding all surface areas of the solid

Your answer:

Finding the area of a circle

Correct answer:

Finding the volume of a solid by taking a cross sectional of it and calculating the volume by adding infinitely many of these cross sections

Explanation:

The disc method allows us to find the volume of a solid in a 2 dimensional space by taking the cross section of a solid. When taking the cross section, you are slicing perpendicular to the axis of rotation (usually either x or y axis). Then we sum infinitely many of these cross sections to obtain a value for the volume, sort of like integrating under the curve.

Flashcards: Apply the Revolving Disc Method and Washer Method

What is the formula for the disc method?

$V = \pi\int _a^b f(x)^2 dx$ $\displaystyle V = \pi\int _a^b f(x)^2 dx$

$V = \pi r^2\int_a^b f(x)^2 dx$ $\displaystyle V = \pi r^2\int_a^b f(x)^2 dx$

$V = \int_a^b \pi r^2 h dr$ $\displaystyle V = \int_a^b \pi r^2 h dr$

$V = \pi r^2 h$ $\displaystyle V = \pi r^2 h$

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Flashcards: Apply the Revolving Disc Method and Washer Method

What is the formula for the disc method?

Your answer:

$V = \pi r^2\int_a^b f(x)^2 dx$ $\displaystyle V = \pi r^2\int_a^b f(x)^2 dx$

Your answer:

$V = \int_a^b \pi r^2 h dr$ $\displaystyle V = \int_a^b \pi r^2 h dr$

Your answer:

$V = \pi r^2 h$ $\displaystyle V = \pi r^2 h$

Correct answer:

$V = \pi\int _a^b f(x)^2 dx$ $\displaystyle V = \pi\int _a^b f(x)^2 dx$

Explanation:

The disc method is based on the volume of a cylinder, $V = \pi r^2 h$ $\displaystyle V = \pi r^2 h$ . In the formula for the disc method, $\displaystyle V$ is the volume of the solid, $\displaystyle a$ is the smallest value of $\displaystyle x$ of f(x) $\displaystyle f(x)$ , $\displaystyle b$ is the largest value of $\displaystyle x$ of f(x) $\displaystyle f(x)$ , f(x) $\displaystyle f(x)$ is the radius of the disc, and $\displaystyle dx$ is the height of the disc.

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