Question

Help ASAP! 20 Points!

A cylinder and a cone have the same diameter: 10 inches. The height of the cylinder and the cone is the same: 12 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

Volume of cylinder is 3 times of volume of cone having same base diameter and same height.

Solution:

Given that

A cylinder and A cone have the same diameter = 10 inches and same height = 12 inches

Need to find the relationship between volume of cylinder and cone.

Let’s calculate volume of each object separately first.

Calculation of volume of cylinder :

Formula of volume of cylinder is given as:

`V_(c y)=\pi r^(2) h`

Where π=3.14

`\text { radius } r=\frac{\text {diameter}}{2}=(10)/(2)=5 \text { inches }`

height h = 12 inches

On substituting given values in formula of cylinder we get

`\begin{array}{l}{V_(c y)=3.14 * 5^(2) * 12=942 \text { cubic inches }} \\\\ {\text { Volume of cylinder }=V_(c y)=942 \text { cubic inches }}\end{array}`

Calculation of volume of cone:

Formula of volume of cone is given as:

`V_(c o)=(\pi r^(2) h)/(3)`

Here π=3.14

`\begin{array}{l}{\text { radius } r=\frac{\text { diameter }}{2}=(10)/(2)=5 \text { inches }} \\\\ {\text { height } \mathrm{h}=12 \text { inches }}\end{array}`

On substituting given values in formula of cone we get

`V_(c o)=(3.14 * 5^(2) * 12)/(3)=314 \text { cubic inches }`

`\text { Volume of cone }=V_(c o)=314 \text { cubic inches }`

On comparing the two volumes we get

`V c y: V c o=942: 314=3: 1`

Hence can conclude that Volume of cylinder is 3 times of volume of cone having same base diameter and same height.