The diagram shows a cologne bottle that consists of a cylindrical base and a hemispherical top. write an expression for cylinders volume and hemispherical top. h= 10cm; r=5cm
The volume of a cylinder is pi*r^2*h. For the hemisphere, it is (2/3) pi r^3.
Your question is not clear about whether the two are to be added.
To find the volume of the cylindrical base, we can use the formula for the volume of a cylinder, which is given by Vcylinder = πr²h, where r is the radius of the base and h is the height.
Given that the radius of the base, r, is equal to 5 cm, and the height of the cylinder, h, is equal to 10 cm, we can substitute these values into the formula:
Vcylinder = π(5²)(10)
Vcylinder = π(25)(10)
Vcylinder = 250π cm³
Therefore, the expression for the volume of the cylindrical base is 250π cm³.
To find the volume of the hemispherical top, we can use the formula for the volume of a sphere, since a hemisphere is half of a sphere. The formula is given by Vsphere = (4/3)πr³, where r is the radius.
Given that the radius of the hemisphere is equal to 5 cm, we can substitute this value into the formula:
Vsphere = (4/3)π(5³)
Vsphere = (4/3)π(125)
Vsphere = (4/3)(125π)
Vsphere = 500π/3 cm³
Therefore, the expression for the volume of the hemispherical top is 500π/3 cm³.
To find the volume of the cylindrical base, you need to use the formula for the volume of a cylinder, which is given by V = πr^2h, where π is approximately 3.14, r is the radius of the base, and h is the height of the cylinder.
In this case, the height of the cylindrical base is given as 10 cm and the radius is given as 5 cm. Plugging these values into the formula, we obtain:
V_cylinder = π(5^2)(10) = 250π cm^3
So the expression for the volume of the cylindrical base is 250π cm^3.
Next, let's consider the hemispherical top. The volume of a hemisphere can be calculated using the formula V = (2/3)πr^3, where r is the radius of the hemisphere.
In this case, the radius of the hemispherical top is also given as 5 cm. Substituting this value into the formula, we get:
V_hemisphere = (2/3)π(5^3) = 250π/3 cm^3
Thus, the expression for the volume of the hemispherical top is 250π/3 cm^3.