If Sa=2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex] then the surface area is π[tex]r^{2} h[/tex] and volume is
(rh-2h)/2r.
Given Sa=2πrh+2π[tex]r^{2} v[/tex]=π[tex]r^{2}h[/tex].
We have to find surface area and volume from the given expression.
Volume is basically amount of substance a container can hold in its capacity.
First we will find the value of v from the expression. Because they are in equal to each other, we can easily find the value of v.
2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}[/tex]h
Keeping the term containing v at left side and take all other to right side.
2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex]-2πrh
v=(π[tex]r^{2}[/tex]h-2πrh)/2π[tex]r^{2}[/tex]
v=π[tex]r^{2} h[/tex]/2π[tex]r^{2}[/tex]-2πrh/2π[tex]r^{2}[/tex]
v=h/2-h/r
v=h(r-2)/2r
Put the value of v in Sa=2πrh+2π[tex]r^{2} v[/tex]
Sa=2πrh+2π[tex]r^{2}[/tex]*h(r-2)/2r
=2πrh+2πrh(r-2)/2
=2πrh+πrh(r-2)
=2πrh+π[tex]r^{2}[/tex]h-2πrh
=π[tex]r^{2}[/tex]h
Hence surface area is π[tex]r^{2}[/tex]h and volume is h(r-2)/2.
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