Cones, Cylinders, & Spheres Unit Test
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Question
Suppose a sphere, cylinder, and cone all share the same radius and the cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone?(1 point)
Responses
1 cylinder = 2 cones + 1 sphere
1 cylinder = 2 cones + 1 sphere
sphere - cone = cylinder
sphere - cone = cylinder
3 cones = 1 cylinder
3 cones = 1 cylinder
sphere = cylinder + cone
sphere = cylinder + cone
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The correct answer is: 1 cylinder = 2 cones + 1 sphere
The volume of a sphere is 48 m3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)
m3
To find the volume of the cylinder, we first need to find the radius of the sphere. We can do this by using the formula for the volume of a sphere:
V = (4/3)πr^3
Rearranging this formula and plugging in the given volume (48 m^3), we can solve for the radius:
48 = (4/3)πr^3
36 = πr^3
r^3 = 36/π
r = (36/π)^(1/3)
Now, since the height of the cylinder is equal to the diameter of the sphere, we know that the height of the cylinder is twice the radius. Therefore, the height (h) of the cylinder is 2 * [(36/π)^(1/3)].
Finally, we can use the formula for the volume of a cylinder:
V = πr^2h
Plugging in the values, we get:
V = π[(36/π)^(1/3)]^2 * 2[(36/π)^(1/3)]= 2 * (36/π)^(2/3) * (36/π)^(1/3)
V = 2 * (36/π)^(3/3)
V = 2 * (36/π)
V = 72/π
So, the volume of the cylinder is 72/π m^3.