Question

Sa = 2(pi)(r)(h) + 2(pi)(r^2) v = (pi)(r^2)(h) find the surface area and the volume.

Answer 1

If Sa=2πrh+2π$r^{2}$v=π$r^{2}h$ then the surface area is π$r^{2} h$ and volume is

(rh-2h)/2r.

Given Sa=2πrh+2π$r^{2} v$=π$r^{2}h$.

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$r^{2}$v=π$r^{2}$h

Keeping the term containing v at left side and take all other to right side.

2π$r^{2}$v=π$r^{2}h$-2πrh

v=(π$r^{2}$h-2πrh)/2π$r^{2}$

v=π$r^{2} h$/2π$r^{2}$-2πrh/2π$r^{2}$

v=h/2-h/r

v=h(r-2)/2r

Put the value of v in Sa=2πrh+2π$r^{2} v$

Sa=2πrh+2π$r^{2}$*h(r-2)/2r

=2πrh+2πrh(r-2)/2

=2πrh+πrh(r-2)

=2πrh+π$r^{2}$h-2πrh

=π$r^{2}$h

Hence surface area is π$r^{2}$h and volume is h(r-2)/2.

Learn more about surface area at brainly.com/question/16519513

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