Question

Help ASAP! 20 Points!

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

$\text { radius } r=\frac{\text {diameter}}{2}=\frac{10}{2}=5 \text { inches }$

height h = 12 inches  

On substituting given values in formula of cylinder we get

$\begin{array}{l}{V_{c y}=3.14 \times 5^{2} \times 12=942 \text { cubic inches }} \\\\ {\text { Volume of cylinder }=V_{c y}=942 \text { cubic inches }}\end{array}$

Calculation of volume of cone:

Formula of volume of cone is given as:

$V_{c o}=\frac{\pi r^{2} h}{3}$

Here π=3.14

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

On substituting given values in formula of cone we get

$V_{c o}=\frac{3.14 \times 5^{2} \times 12}{3}=314 \text { cubic inches }$

$\text { Volume of cone }=V_{c o}=314 \text { cubic inches }$

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.