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.

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.