Calculus Simulation 2

VOLUMES OF REVOLUTION - DISK METHOD

To rotate grid, click and drag

REVOLVE REGION

# OF DISKS

AXIS OF REVOLUTION

x y

Region 1

Region 2

Region 3

\begin{matrix} Region 1 y = - \frac{10}{12} \sqrt{(12^{2} - x^{2})}, y = 0 \end{matrix}

\begin{matrix} Volume \int_{a}^{b} π y^{2} d x \approx 0 \end{matrix}

\begin{matrix} Volume \int_{c}^{d} π x^{2} d y \approx 0 \end{matrix}

\begin{matrix} Region 2 y = (x - 3)^{2} \\ when x \geq 3, x = 0 y = 4 \end{matrix}

\begin{matrix} Volume \int_{a}^{b} π y^{2} d x \approx 0 \end{matrix}

\begin{matrix} Volume \int_{c}^{d} π x^{2} d y \approx 0 \end{matrix}

\begin{matrix} Region 3 y = x^{2} - 2 x + 2, \\ x = 0, x = 3 and y = 0 \end{matrix}

\begin{matrix} Volume \int_{a}^{b} π y^{2} d x \approx 0 \end{matrix}

\begin{matrix} Volume \int_{c}^{d} π x^{2} d y \approx 0 \end{matrix}

\begin{array}{ll} Number of Disks : & 0 \\ Width of Disks : & 0.00 \\ Sum of Volume of Disks \approx & 0.00{units}^{3} \end{array}

Note

Note that the disk method is not applicable here since not all the slices of the solid generated are disks. However, you will be able to compute its volume using washer method which will be covered in the next module.

YOU WILL LEARN ABOUT:

Click on the tabs on the right to watch videos on rotating a region about the x-axis and y-axis.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.

Select any of the regions from the three options given at the bottom left-hand corner of the screen. Rotate the region around either x or y axis to obtain the solid and answer the following questions.