Please help.. A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11ft^3

Which equation gives the volume of the sphere?

^(Answers above on picture)^

9514 1404 393

  (d)  2/3(11)

Step-by-step explanation:

The height of the cylinder is h=2r, so the volume of the cylinder in terms of radius is ...

  V = πr^2·h = πr^2·(2r) = 2πr^3

The volume of the sphere is given by the formula ...

  V = (4/3)πr^3

So, the ratio of the sphere volume to the cylinder volume is ...

  sphere volume / cylinder volume = ((4/3)πr^3)/(2πr^3) = (4/3)/2 = 2/3

That is, the sphere volume is ...

  sphere volume = (2/3) × (cylinder volume)

  V = (2/3)(11)

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24