We know that
the distance from the centroid of the triangle to one of the vertices is the radius of the circle <span>required to inscribe an equilateral triangle.
[distance </span>centroid of the triangle to one of the vertices]=(2/3)*h
h=the <span>altitude of the equilateral triangle-----> 5.196 in
so
</span>[distance centroid of the triangle to one of the vertices]=(2/3)*5.196
[distance centroid of the triangle to one of the vertices]=3.464 in----> 3.5 in
the radius is equal to the distance of the centroid of the triangle to one of the vertices
hence
the radius is 3.5 in
the answer is
the radius is 3.5 in
The formula for the surface area of a cylinder is:
2<span>π</span><span>r</span><span>h </span><span>+ </span><span>2</span><span>π</span><span>r^</span><span>2
If we substitute in the measurements that we know, you get:
2</span><span>

(3.5) (14) + 2</span><span>

(3.5)^2
If we simplify this expression, we get:
98</span><span>

+ 24.5</span><span>

If you simplify once more, you get
122.5</span><span>

or </span><span>≈ 384.85
Therefore, the surface area is 122.5</span>

or about 384.85<span>
</span>
D is the answer to your question