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
50/3 π cm^3
50/3 π cm^3
25 π cm3
25 π cm^3
25/2 π cm3
25/2 π cm^3
25/6 π cm3
To find the volume of a cone, you can use the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height. In this case, the volume of the cone is given as 25/3π cm^3.
Let's label the radius of the cone as r and the height as h. We are also given that the height of the cone is equal to the sphere's diameter, which means h = 2r.
Substituting the value for h in terms of r into the volume formula:
(25/3)π = (1/3)πr²(2r)
25/3 = 2r³
r³ = (25/3) * (3/2)
r³ = 25/2
Now, take the cube root of both sides to solve for r:
r = ∛(25/2)
r ≈ 2.924 cm
Now that we have the radius of the sphere, we can calculate its volume using the formula V = (4/3)πr³:
V = (4/3)π(2.924)³
V ≈ 50.01π cm^3
Rounded to the nearest hundredth, the volume of the sphere is approximately 50.01π cm^3.
The correct response from the given options is 50/3 π cm^3.
The formula vw=f⋅λ
=
⋅
describes the relationship between the speed of a wave (vw
), and its frequency (f
) and wavelength (λ
).
For example, if a wave has a frequency of 120 Hz and a wavelength of 5m, it would have a speed of 600 m/s.
In one or two sentences, describe what would happen to the frequency of this wave if the wavelength is increased to 10m but the speed stays the same at 600 m/s.
(2 points)
Help plzz!!!
The volume of a cone is 25/3 π cm3. What is the volume of a sphere if its radius is the same as the cones and the height of the cone is equal to the sphere’s diameter? (1 point)
Responses
50/3 π cm^3
50/3 π cm^3
25 π cm3
25 π cm^3
25/2 π cm3
25/2 π cm^3
25/6 π cm3
If the wavelength of the wave is increased to 10m while the speed remains the same, the frequency of the wave would decrease because frequency and wavelength are inversely proportional.
To find the volume of a sphere, we need to know the formula for the volume of a sphere.
The formula for the volume of a sphere is V = (4/3)πr^3, where V represents the volume and r represents the radius.
In this case, we are given that the radius of the cone and the sphere is the same. Let's denote it as r.
We are also given that the height of the cone is equal to the sphere's diameter. The diameter of the sphere is twice the radius, so the height of the cone is 2r.
Now, we need to find the volume of the sphere with the given information.
First, let's find the volume of the cone:
V_cone = 253π cm^3
The formula for the volume of a cone is V_cone = (1/3)πr^2h, where h represents the height.
Substituting the given values:
253π = (1/3)πr^2(2r)
Simplifying:
253π = (2/3)πr^3
Dividing both sides by (2/3)π:
(3/2)(253π) = r^3
r^3 = (3/2)(253π)
r^3 = (759/2)π
Now, let's find the volume of the sphere:
V_sphere = (4/3)πr^3
Substituting the value of r^3:
V_sphere = (4/3)π((759/2)π)
Simplifying:
V_sphere = (4/3)((759/2)π)^2
V_sphere = (4/3)((759)^2/4)π^2
V_sphere = (759^2/3)π^2
Therefore, the volume of the sphere is (759^2/3)π cm^3, which can be further simplified if needed.
To find the volume of a cone, you can use the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height. In this case, the volume of the cone is given as 253π cm^3.
Let's label the radius of the cone as r and the height as h. We are also given that the height of the cone is equal to the sphere's diameter, which means h = 2r.
Substituting the value for h in terms of r into the volume formula:
V = (1/3)πr²(2r)
V = (2/3)πr³
We know that the volume of the cone is 253π cm^3:
253π = (2/3)πr³
To isolate r³, divide both sides by (2/3)π:
r³ = (3/2)(253π/π)
r³ = 3/2 * 253
r³ = 379.5
Now, take the cube root of both sides to solve for r:
r = ∛(379.5)
r ≈ 7.68 cm
Now that we have the radius of the sphere, we can calculate its volume using the formula V = (4/3)πr³:
V = (4/3)π(7.68)³
V ≈ 25.99π cm^3
Rounded to the nearest hundredth, the volume of the sphere is approximately 25.99π cm^3.
None of the given response options match this answer exactly.