Suppose 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)
Responses
cylinder = sphere – cone
cylinder = sphere – cone
sphere = cylinder + cone
sphere = cylinder + cone
cone = sphere – cylinder
cone = sphere – cylinder
cone = cylinder – sphere
9 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?(1 point)
Responses
12 cm3
12 cm cubed
54 cm3
54 cm cubed
18 cm3
18 cm cubed
24 cm3
Responses
12 cm3
12 cm cubed
54 cm3
54 cm cubed
18 cm3
18 cm cubed
24 cm3
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.
Given that the volume of the cylinder is 36 cm^3, we have Vcylinder = 36 cm^3.
We also know that the height of the cylinder is equal to the diameter of the sphere, and since the radius of the cylinder is the same as the radius of the sphere, we can say that the radius of the sphere, rsphere, is equal to the height of the cylinder, hcylinder.
Therefore, we can write rsphere = hcylinder.
The volume of the sphere is given by the formula V = (4/3)πr^3, where r is the radius.
Since rsphere = hcylinder, we can substitute rsphere with hcylinder in the formula for the volume of the sphere:
Vsphere = (4/3)π(rsphere)^3 = (4/3)π(hcylinder)^3
If we substitute the value of hcylinder with the volume of the cylinder (Vcylinder = 36 cm^3), we get:
Vsphere = (4/3)π(36)^3 = (4/3)π(216) = 288π cm^3
Therefore, the volume of the sphere is 288π cm^3, or approximately 904.78 cm^3.
Given that the volume of the cylinder is 36 cm^3, we have Vcylinder = 36 cm^3.
We also know that the height of the cylinder is equal to the diameter of the sphere, and since the radius of the cylinder is the same as the radius of the sphere, we can say that the radius of the sphere, rsphere, is equal to the height of the cylinder, hcylinder.
Therefore, we can write rsphere = hcylinder.
The volume of the sphere is given by the formula V = (4/3)πr^3, where r is the radius.
Since rsphere = hcylinder, we can substitute rsphere with hcylinder in the formula for the volume of the sphere:
Vsphere = (4/3)π(rsphere)^3 = (4/3)π(hcylinder)^3
If we substitute the value of hcylinder with the volume of the cylinder (Vcylinder = 36 cm^3), we get:
Vsphere = (4/3)π(36)^3 = (4/3)π(216) = 288π cm^3
Therefore, the volume of the sphere is 288π cm^3, or approximately 904.78 cm^3.
so whats the answer
The volume of the sphere is approximately 904.78 cm^3.
The volume of a cone is 253 π cm3 . What is the volume of a sphere if its radius is the same as the cone’s and the height of the cone is equal to the sphere’s diameter?(1 point)
We know that the volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 253π cm^3, we have Vcone = 253π cm^3.
We also know that the height of the cone is equal to the diameter of the sphere, and since the radius of the cone is the same as the radius of the sphere, we can say that the radius of the sphere, rsphere, is equal to the height of the cone, hcone.
Therefore, we can write rsphere = hcone.
The volume of the sphere is given by the formula V = (4/3)πr^3, where r is the radius.
Since rsphere = hcone, we can substitute rsphere with hcone in the formula for the volume of the sphere:
Vsphere = (4/3)π(rsphere)^3 = (4/3)π(hcone)^3
If we substitute the value of hcone with the volume of the cone (Vcone = 253π cm^3), we get:
Vsphere = (4/3)π(253π)^3 = (4/3)π(253^3π^3) = (4/3)π(16129π^3) = 21505π^4 cm^3
Therefore, the volume of the sphere is 21505π^4 cm^3.
Given that the volume of the cone is 253π cm^3, we have Vcone = 253π cm^3.
We also know that the height of the cone is equal to the diameter of the sphere, and since the radius of the cone is the same as the radius of the sphere, we can say that the radius of the sphere, rsphere, is equal to the height of the cone, hcone.
Therefore, we can write rsphere = hcone.
The volume of the sphere is given by the formula V = (4/3)πr^3, where r is the radius.
Since rsphere = hcone, we can substitute rsphere with hcone in the formula for the volume of the sphere:
Vsphere = (4/3)π(rsphere)^3 = (4/3)π(hcone)^3
If we substitute the value of hcone with the volume of the cone (Vcone = 253π cm^3), we get:
Vsphere = (4/3)π(253π)^3 = (4/3)π(253^3π^3) = (4/3)π(16129π^3) = 21505π^4 cm^3
Therefore, the volume of the sphere is 21505π^4 cm^3.
which one of the four is the answer
I apologize for the confusion. The correct answer is not provided in the given options. The volume of the sphere cannot be determined solely based on the information given about the cone.
2 answers