Can anyone help me on my Volume Practice Worksheet?

Question

My teache gave us this worksheet with only 4 math problems. We did math problems similar to this in class today but it was not exactly like this. She gave us the base, length, and height and we just had to double or triple some. That's it. I've never done and she's never teached us how to find the base and height for volume of a shape before.

π= pi

1. If a cylinder has a volume of 45π, what is the volume of a cone with the same base and height?
2. A cylinder has a volume of 40π. If the radius is doubled and the height is tripled, what is the new volume of the cylinder?
3. A cube has a volume of 125 in³ . If all side lengths are doubled, what is the new volume?
4. A cone has a volume of 75π. If the radius of the circle base is 5, what is the height of the cone?

Answer 1

V(cyl) = B*H,  V(cone) = 1/3 B*H.  1/3(45 pi) = 15 pi.

V(cyl) = B*H,  B = pi r^2.  V(cyl, new) = pi (2r)^2 * 3H = 4 pi r^2 * 3H = 12 pi r^2 *H = 12 B*H =

12 (40 pi) = 480 pi.

V(cube) = x^3.  V(new cube) = (2x)^3 = 8x^3.  From original cube x=5. New volume = 8 (125 in^3)=

1000 in^3.

V(cone) = 1/3 *B*H,  H = V(cone)/(1/3)B  =  V(cone)/(1/3) pi r^2 = (75 pi)/((1/3) pi 5^2)  = 9

 

Answer 2

1. Volume of a cylinder is πr²h, volume of a cone is (1/3)nr²h. the trick here is to treat r²h as though it was one value. So, 45n = nr²h means that r²h = 45. Now just plug that in to the cone formula.

2. Using the same formula as above for a cylinder, substitute factors of 2 and 3 in for each respective dimension:

If nr²h = 40 then when you substitute in 2r and 3h you get

n(2r)²(3h) = n(4r²)(3h) = 12nr²h

Now just use the original value you got from the question to get the answer.

3. This is similar to number two, use the formula for the volume of a cube and plug in the new dimensions to arrive at the answer:

V_cube = l³. The new V = (2l)³ = 8l³.

4. This one involves substituting the values given into the equation for the volume of a cone so that you are solving a single equation with one unknown:

(1/3)nr²h = 75n

You're given the radius so all that is left is to plug in the value and solve for h. hope that helped.