To find the total volume of the toy model, we need to add the volumes of the cone, cylinder, and hemisphere.
The volume of a cone is given by the formula V = (1/3)Ï€r^2h, where r is the base radius and h is the height.
We are given that the volume of the cone is 5x, so we can write:
5x = (1/3)Ï€r^2(2r)
Simplifying this equation, we have:
15x = πr^3
Now, the volume of a cylinder is given by the formula V = πr^2h, where r is the base radius and h is the height.
We are given that the height of the cylinder is 2r, so we can write:
V_cylinder = πr^2(2r) = 2πr^3
Finally, the volume of a hemisphere is given by the formula V = (2/3)Ï€r^3, where r is the radius.
We have a hemisphere with the same radius as the cylinder, so we can write:
V_hemisphere = (2/3)Ï€r^3
To find the total volume of the toy model, we add the volumes of the cone, cylinder, and hemisphere:
Total volume = V_cylinder + V_cone + V_hemisphere
= 2Ï€r^3 + 5x + (2/3)Ï€r^3
Combining like terms, we have:
Total volume = (2Ï€/3)r^3 + 5x + (2/3)Ï€r^3
To simplify further, we can factor out (2/3)Ï€r^3 and combine it with the other term:
Total volume = [(2Ï€/3)r^3 + (2/3)Ï€r^3] + 5x
= (4/3)Ï€r^3 + 5x
Therefore, the total volume of the toy model is (4/3)Ï€r^3 + 5x.
None of the given options match this expression, so none of the provided answers are correct.