The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
In this case, the volume of the cone is 253π cm^3, and the height is equal to the sphere's diameter. Let's assume the radius of the cone and the sphere is r.
The volume of the cone can be written as 253π = (1/3) * π * r^2 * 2r
Simplifying this equation, we get 253 = (2/3) * r^3
To find the volume of the sphere, we use the formula V = (4/3) * π * r^3. Since the radius is the same as the cone's radius, we can substitute r^3 in the volume equation for the sphere with (3/2) * 253, which is the value we found for r^3 in the cone's volume equation.
V_sphere = (4/3) * π * (3/2 * 253)
= (4/3) * π * (379.5)
= 503π cm^3
Therefore, the volume of the sphere is 503π 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)
Responses
252 π cm3
Start Fraction 25 over 2 End Fraction pi cm cubed
503 π cm3
Start Fraction 50 over 3 End Fraction pi cm cubed
256 π cm3
Start Fraction 25 over 6 End Fraction pi cm cubed
25 π cm3
25 pi cm cubed
5 answers
A sculptor created a design by carving a cone out of a cylinder. The cone and cylinder share the same radius and height. If the volume of the cylinder before removing the cone is 54 in.3 , what is the volume of the amount remaining?(1 point)
Responses
36 in.3
36 in. cubed
27 in.3
27 in. cubed
18 in.3
18 in. cubed
40 in.3
Responses
36 in.3
36 in. cubed
27 in.3
27 in. cubed
18 in.3
18 in. cubed
40 in.3
The volume of a cylinder is given by the formula V = π * r^2 * h, where r is the radius and h is the height.
In this case, the volume of the cylinder is 54 in^3, and the cone carved out has the same radius and height. Let's assume the radius of the cylinder and cone is r, and the height is h.
Since the volume of the cone is carved out from the cylinder, the remaining volume is the volume of the cylinder minus the volume of the cone.
The volume of the cylinder is 54 in^3, which can be written as π * r^2 * h.
The volume of the cone can be calculated using the formula (1/3) * π * r^2 * h.
The remaining volume is therefore:
Volume remaining = Volume of Cylinder - Volume of Cone
= (π * r^2 * h) - [(1/3) * π * r^2 * h]
= (2/3) * π * r^2 * h
Since the radius and height of the cylinder and cone are the same, we can simplify this to:
Volume remaining = (2/3) * π * r^2 * h
= (2/3) * (π * r^2 * h)
= (2/3) * 54
= 36 in^3
Therefore, the volume of the remaining amount is 36 in^3.
In this case, the volume of the cylinder is 54 in^3, and the cone carved out has the same radius and height. Let's assume the radius of the cylinder and cone is r, and the height is h.
Since the volume of the cone is carved out from the cylinder, the remaining volume is the volume of the cylinder minus the volume of the cone.
The volume of the cylinder is 54 in^3, which can be written as π * r^2 * h.
The volume of the cone can be calculated using the formula (1/3) * π * r^2 * h.
The remaining volume is therefore:
Volume remaining = Volume of Cylinder - Volume of Cone
= (π * r^2 * h) - [(1/3) * π * r^2 * h]
= (2/3) * π * r^2 * h
Since the radius and height of the cylinder and cone are the same, we can simplify this to:
Volume remaining = (2/3) * π * r^2 * h
= (2/3) * (π * r^2 * h)
= (2/3) * 54
= 36 in^3
Therefore, the volume of the remaining amount is 36 in^3.
An engineer wants to know the volume of the following object composed of a hemisphere and a cone. She knows the height of the cone is equal to the diameter of the hemisphere, and the volume of the cone is 12 m3 . What is the volume of the whole object?(1 point)
Responses
There is not enough information to say.
There is not enough information to say.
36 m3
36 m cubed
24 m3
24 m cubed
18 m3
Responses
There is not enough information to say.
There is not enough information to say.
36 m3
36 m cubed
24 m3
24 m cubed
18 m3
To find the volume of the whole object, we need the radius of either the hemisphere or the cone. However, the radius is not given in the problem statement.
Therefore, there is not enough information to determine the volume of the whole object.
Therefore, there is not enough information to determine the volume of the whole object.
1 answer