Volume of Cones, Cylinders, and Spheres Quick Check1 of 51 of 5 ItemsQuestionSuppose a sphere, cylinder, and cone all share the same radius. 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)Responsessphere = cylinder + conesphere = cylinder + conecone = cylinder – spherecone = cylinder – spherecone = sphere – cylindercone = sphere – cylindercylinder = sphere – cone
3 answers
cone = cylinder – sphere
Use the relationship among the formulas for the volumes of cones, cylinders, and spheres to solve the following problem. The volume of a cylinder is 36 cm3. What is the volume of a sphere if its radius is the same as the cylinder’s and the height of the cylinder is equal to the sphere’s diameter?
We know that the volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
In this problem, we are given that the volume of the cylinder is 36 cm^3. Let's assume that the radius of the cylinder is "r" and the height is also "r" (because it is equal to the sphere's diameter).
Therefore, we can write the equation as 36 = πr^2 * r
Simplifying this equation, we get:
36 = πr^3
To solve for the volume of the sphere, we need to find the radius of the sphere. Since the height of the cylinder is equal to the sphere's diameter, we know that the radius of the sphere is also "r".
So, the volume of the sphere is given by the formula V = (4/3)πr^3.
Substituting the value of r from the equation above, we get:
V = (4/3)π * 36
Simplifying this equation, the volume of the sphere is:
V = 48π cubic cm.
Therefore, the volume of the sphere is 48π cubic cm.
In this problem, we are given that the volume of the cylinder is 36 cm^3. Let's assume that the radius of the cylinder is "r" and the height is also "r" (because it is equal to the sphere's diameter).
Therefore, we can write the equation as 36 = πr^2 * r
Simplifying this equation, we get:
36 = πr^3
To solve for the volume of the sphere, we need to find the radius of the sphere. Since the height of the cylinder is equal to the sphere's diameter, we know that the radius of the sphere is also "r".
So, the volume of the sphere is given by the formula V = (4/3)πr^3.
Substituting the value of r from the equation above, we get:
V = (4/3)π * 36
Simplifying this equation, the volume of the sphere is:
V = 48π cubic cm.
Therefore, the volume of the sphere is 48π cubic cm.
1 answer