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Bot GPT 3.5 The volume of the whole object can be calculated by summing the volumes of the hemisphere and the cone.
The volume of a hemisphere is given by (2/3)Ï€r^3, where r is the radius of the hemisphere.
The volume of a cone is given by (1/3)Ï€r^2h, where r is the radius of the base and h is the height of the cone.
In this case, we are given that the height of the cone is equal to the diameter of the hemisphere, which means h = 2r.
We are also given that the volume of the cone is 12 m^3.
To find the volume of the whole object, we need to find the radius of the hemisphere.
Since the height of the cone is equal to the diameter of the hemisphere, the radius of the hemisphere is equal to half the height of the cone, which is r = h/2.
Substituting this value of r into the formula for the volume of a hemisphere, we get the volume of the hemisphere as (2/3)Ï€(h/2)^3 = (1/6)Ï€h^3.
The volume of the whole object is then (1/6)Ï€h^3 + (1/3)Ï€r^2h = (1/6)Ï€h^3 + (1/3)Ï€(h/2)^2h = (1/6)Ï€h^3 + (1/12)Ï€h^3 = (1/4)Ï€h^3.
Since we are given that the volume of the cone is 12 m^3, we can substitute this value for the volume of the whole object and solve for h.
(1/4)Ï€h^3 = 12
Multiplying both sides by 4/Ï€, we get h^3 = 48/Ï€
Taking the cube root of both sides, we get h = (48/Ï€)^(1/3)
Substituting this value of h back into the formula for the volume of the whole object, we get
V = (1/4)Ï€[(48/Ï€)^(1/3)]^3 = (1/4)Ï€(48/Ï€) = 12 m^3.
Therefore, the volume of the whole object is 12 m^3. Answer: 12 m3.
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