Acompany is designing a label for a new cylindrical container. the container and some of its dimensions are shown. the label will be the same height as the container and will not overlap itself and will cover the entire side of the cylinder. what will be the area of the label?

The area of the label would be 52.5π cm², or 164.85 cm².

The information we're given is the area of the circular base and the height.  We know that the formula for the area of a circle is A=πr².  Using this we have:

9π=πr²

Divide both sides by π:
9π/π = πr²/π
9=r²

Take the square root of both sides:
√9 = √r²
3 = r

The length of the label will be the circumference of the circle.  The formula for circumference is C=πd, and we know that d = 2r, so we have:
C=π(2*3)
C=6π

Now we have both dimensions of the label:

A=l*w
A=6π*8.75=52.5 cm²

If you use 3.14 for π, you get 164.85 cm²