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Thepotemich [5.8K]
3 years ago
7

Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is

Mathematics
1 answer:
damaskus [11]3 years ago
5 0
To find the area of the cylinder we need to find its volume first. Remember that the formula for the volume of a cylinder is V= \pi r^{2} h
where:
V is the volume 
r is the radius 
h is the height 
From the question we know that A=175 and h=7. Lets replace those values in our volume formula:
175= \pi r^{2} 7
Now we can solve for r to find our radius:
r^{2} = \frac{175}{7 \pi }
r^{2} = \frac{25}{ \pi }
r= \sqrt{ \frac{25}{ \pi } }
r= \frac{5}{ \sqrt{ \pi } }

Now that we know the radius, we can use the formula for the area of a cylinder A=2 \pi rh+2 \pi r^{2}
where:
A is the area
r is the radius 
h is the height
We know now that r= \frac{5}{ \sqrt{ \pi } } and h=7, so lets replace those values in our area formula:
A=2 \pi ( \frac{5}{ \sqrt{ \pi } } )(7)+2 \pi ( \frac{5}{ \sqrt{ \pi } })^{2}
A= \frac{70 \pi }{ \sqrt{ \pi } } +50
A=174.07

We can conclude that the area of a cylinder that has a volume of 175 cubic units and a height of 7 units is 174.07 square units.

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