Question 1158742
The height of a right circular cylinder is 1.5 times the radius of the base.
What is the ratio of the total surface area to the lateral (curved) surface area
of the cylinder?
<pre>
{{{S=2*pi*r*h}}}  <-- lateral (curved) surface area
</pre>The height of a right circular cylinder is 1.5 times the radius of the base.<pre>So h = 1.5r and therefore

{{{S=2*pi*r*(1.5r)}}}

{{{S=3*pi*r^2}}}  <-- lateral (curved) surface area</pre>What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?<pre>Total surface area =

{{{matrix(1,9,
(matrix(3,1,Total,surface,area)),
"",
""="",
"",
(matrix(4,1,lateral,"(curved)",surface,area)),
""+"",
(matrix(3,1,Area,of,top)),
""+"",
(matrix(3,1,Area,of,bottom)) )}}}

{{{matrix(1,9,
(matrix(3,1,Total,surface,area)),
"",
""="",
"",
3pi*r^2,
""+"",
pi*r^2,
""+"",
pi*r^2 )}}}

{{{matrix(1,5,
(matrix(3,1,Total,surface,area)),
"",
""="",
"",
5pi*r^2 )}}}
</pre>What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?<pre>
{{{matrix(1,9,
(matrix(1,3,Total,surface,area))/(matrix(1,4,lateral,"(curved)",surface,area)),
"",
""="",
"",
5pi*r^2/(3pi*r^2),
"",
""="",
"",
5/3)}}}

Edwin</pre>