A cone has a radius of 6 inches and a height of 9 inches
a) calculate the volume of the cone. use pi. as my answer for part a i got 339.92 cubic inches,,,,,,, Is my answer correct ??
I need help doing part b and c.
b) calculate a possible radius and height of a cylinder that has the same volume as the cone.
c) If the radius of the cylinder is the same as the radius of the cone, what is the height of the cylinder?
v = pi/3 r^2 h = pi/3 * 36 * 9 = 108pi
for cylinder,
v = pi r^2 h, so a cylinder 1/3 as high would have the same volume as the cone.
see above. same radius, 1/3 height.
thank you very much - Steve
What is the volume of a cone that has a radius of 9 inches and a height of 16 inches? Use 3.14 for pi
To calculate the volume of a cone, you can use the formula:
V = (1/3) * π * r^2 * h
where V is the volume, π is pi, r is the radius, and h is the height of the cone.
Let's calculate the volume of the cone given the radius (r = 6 inches) and height (h = 9 inches):
V = (1/3) * π * (6^2) * 9
V = (1/3) * 3.14 * 36 * 9
V = (1/3) * 3.14 * 324
V ≈ 339.92 cubic inches
So, your answer for part a is correct.
Now, for part b, we need to find a possible radius and height of a cylinder that has the same volume as the cone.
To find the volume of a cylinder, you can use the formula:
V = π * r^2 * h
Since we want the volume to be the same as the cone, we can set the two formulas equal to each other:
(1/3) * π * 6^2 * 9 = π * r^2 * h
Simplifying the equation, we get:
2 * 36 * 9 = r^2 * h
r^2 * h = 72
Now, we need to find a possible radius and height combination that satisfies this equation. There could be multiple answers. One possible solution is:
r = 4 inches
h = 18 inches
So, for part b, a possible radius and height of a cylinder that has the same volume as the cone is r = 4 inches and h = 18 inches.
Moving on to part c, if the radius of the cylinder is the same as the radius of the cone (r = 6 inches), but we still want the volume to be the same, we can substitute these values into the formula:
r^2 * h = 72
6^2 * h = 72
36 * h = 72
h = 72 / 36
h = 2 inches
So, for part c, if the radius of the cylinder is the same as the radius of the cone, the height of the cylinder would be 2 inches.