Question 1139006
 A hemisphere of diameter {{{10cm}}} is attached to a cylinder of equal diameter. If the total length of the shape is {{{20cm }}}calculate:


A) the surface area of the hemisphere 

given: diameter {{{d=10cm}}}=> radius {{{r=5cm}}}

{{{SA=2pi*r^2}}}
{{{SA=2pi*(5cm)^2}}}
{{{SA=2pi*25cm^2}}}
{{{SA=50pi*cm^2}}}=> exact solution
{{{ SA=157.14cm^2}}}=>approximate solution


B) length of cylinder 

 If the total length of the shape is {{{20cm}}} calculate, the length of cylinder will be difference between  the total length of the shape  and radius of cylinder 

{{{20cm-r=20cm-5cm=15cm}}}


C) surface area of the whole shape 

will be of the hemisphere plus surface area of cylinder (without one base)
 
 surface area of cylinder is:
lateral surface area of cylinder is {{{2pi*rh}}}
area of bottom of cylinder (circle) is {{{r^2*pi}}}

{{{SA[c]=2rpi*h+r^2*pi}}}....plug in {{{r=5cm}}}, {{{h=15cm}}}
{{{SA[c]=2*5cmpi*15cm+(5cm)^2*pi}}}
{{{SA[c]=150pi*cm^2+25cm^2*pi}}}
{{{SA[c]=175pi*cm^2}}}=> exact solution
{{{SA[c]=549.5cm^2}}}=>approximate solution

=>surface area of the whole shape is: 

{{{total=50pi*cm^2+175pi*cm^2=225pi*cm^2}}}=> exact solution

{{{total=157.14cm^2+549.5cm^2=706.64cm^2}}}=>approximate solution