Question

eldted. Go to volume of a cylinder C and volume of a cone e, and complete each step below.Question 1Drag the orange points on the cylinder and the cone to change their radii and heights. (Make sure the Freeze height checkboxes are not checked.)Set equal radii and heights for the cylinder and the cone, and note their respective volumes. Record the volumes for a few sets of heights andradii, and calculate the ratio of the volumes in each case. Remember, make sure the height and radius of the cone and the cylinder are the samein each pair. (You might see some discrepancies in the tool due to rounding of decimals.) Round your calculations for ratio to the hundredthsplace. The first one has been done for you.B 1 vx xFont SizesAA- EEE 들 -V of coneRadius Height Volume of Cone Volume of Cylinder Ratio of Volumes of cylinder)112162,412.77.238.20.332345

Answer 1

The volume of a cone is computed as follows:

$V\text{ of cone}=\pi r^2\frac{h}{3}$

where r is the radius and h is the height of the cone.

The volume of a cylinder is computed as follows:

$V\text{ of cylinder=}\pi r^2h$

where r is the radius and h is the height of the cylinder.

Substituting with r = 1 and h = 1, the volumes are:

$\begin{gathered} V\text{ of cone}=\pi\cdot1^2\cdot\frac{1}{3}=\pi\cdot1\cdot\frac{1}{3}\approx1.05 \\ V\text{ of cylinder=}\pi\cdot1^2\cdot1=\pi\approx3.14 \end{gathered}$

And the ratio of volumes is:

$\frac{V\text{ of cone}}{V\text{ of cylinder }}=\frac{1.05}{3.14}\approx0.33$

Substituting with r = 2 and h = 4, the volumes are:

$\begin{gathered} V\text{ of cone}=\pi\cdot2^2\cdot\frac{4}{3}=\pi\cdot4\cdot\frac{4}{3}\approx16.76 \\ V\text{ of cylinder=}\pi\cdot2^2\cdot4=\pi\cdot4\cdot4\approx50.26 \end{gathered}$

And the ratio of volumes is:

$\frac{V\text{ of cone}}{V\text{ of cylinder }}=\frac{16.76}{50.26}\approx0.33$