What is the volume of a cylinder with a radius of 9 inches and a height of 2 inches? use 3.14 for pi. round your answer to the nearest hundredth.
500.21 cubic inches
508.68 cubic inches
550.45 cubic inches
561.75 cubic inches

Step-by-step explanation:

The volume of a cylinder is defined as

Where is the area of the base and is the height.

In this case, we have a circular cylinder, which means the area of its bottom is circular with a radius of 9 inches. And its height is 2 inches, by given, that is

, . Also we know that .

And the area of a circle is defined as

Replacing the radius, we have

Then, we use this area to find the volume

Therefore, the right answer is the second choice.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: