<PRE><B>Question 1121711</B>
&lt;br&gt;
The total surface area is the area of the base plus the lateral surface area:&lt;br&gt;
{{{(pi)r^2+(pi)(r)(l)}}}&lt;br&gt;
where l is the slant height.&lt;br&gt;
The radius of the cone is 3; and the total surface area is 72pi.  We can plug those numbers into the formula for the total surface area to determine the slant height; then the Pythagorean Theorem will give us the height of the cone.&lt;br&gt;
{{{9(pi)+(pi)(3)(l) = 72(pi)}}}
{{{3(pi)l = 63(pi)}}}
{{{l = 21}}}&lt;br&gt;
{{{3^2+h^2 = 21^2}}}
{{{h^2 = 441-9 = 432}}}
{{{h = 12*sqrt(3)}}}&lt;br&gt;
(a) The height of the cone is 12*sqrt(3)cm.&lt;br&gt;
(b) The radius of the sector is the slant height of the cone: 21 cm.&lt;br&gt;
The circumference of the base of the cone is the arc length of the sector.  The fraction that arc length is of the entire circle is the ratio of the circumference of the cone to the circumference of the circle:&lt;br&gt;
{{{6(pi)/42(pi) = 1/7}}}&lt;br&gt;
(c) The angle of the sector is 1/7 of the full circle: 2pi/7.</PRE>