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:
[tex]V_{c y}=\pi r^{2} h[/tex]
Where π=3.14
[tex]\text { radius } r=\frac{\text {diameter}}{2}=\frac{10}{2}=5 \text { inches }[/tex]
height h = 12 inches
On substituting given values in formula of cylinder we get
[tex]\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}[/tex]
Calculation of volume of cone:
Formula of volume of cone is given as:
[tex]V_{c o}=\frac{\pi r^{2} h}{3}[/tex]
Here π=3.14
[tex]\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}[/tex]
On substituting given values in formula of cone we get
[tex]V_{c o}=\frac{3.14 \times 5^{2} \times 12}{3}=314 \text { cubic inches }[/tex]
[tex]\text { Volume of cone }=V_{c o}=314 \text { cubic inches }[/tex]
On comparing the two volumes we get
[tex]V c y: V c o=942: 314=3: 1[/tex]
Hence can conclude that Volume of cylinder is 3 times of volume of cone having same base diameter and same height.
