Question 865139
You want to find in your textbook or some reference, the formula for surface area of a sphere.  This is {{{4*pi*r^2}}}.


The surface area for the straight side part of a cylinder is {{{h*2pi*r}}}
and
The surface area for the bottom of a cylinder is {{{pi*r^2}}}.


Your exercise referenced shows a straight circular cylinder capped on <b>topped with a half-sphere</b>.  The height, h, of the straight cylinder part is 10 cm; the radius of the base is 7 cm or r; the radius of the half-sphere is also r=7 cm.  Using these, the labeled total height of 17 cm has already been accounted.


The total surface area is the sum of those of the half-sphere, the straight sides, and the bottom base:
{{{(4pi*r^2)/2+2*h*pi*r+pi*r^2}}}
Just simplify and substitute for r and h, and compute.
{{{2pi*r^2+2h*pi*r+pi*r^2}}}
{{{pi(2r^2+2hr+r^2)}}}
{{{pi(3r^2+2*h*r)}}}
SUBSTITUTE THE VALUES:
{{{3.142(3*49+2*10*7)}}}
{{{3.142(147+140)}}}
{{{3.142(287)}}}
{{{highlight(901.754)}}} which should be rounded to {{{highlight(highlight(901.8))}}} cubic centimeters.