Find the volume and the surface of the barrel with base radius 14 and a height of 33 which is given that it's a open hollow cylinder
To find the volume of the barrel, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the base and h is the height.
Given that the base radius (r) is 14 and the height (h) is 33, we can substitute these values into the formula to find the volume:
V = π(14^2)(33)
V = π(196)(33)
V = 6468π
Therefore, the volume of the barrel is 6468π cubic units.
To find the surface area of the barrel, we need to consider both the curved surface area and the areas of the two circular bases.
The curved surface area can be calculated using the formula: A = 2πrh, where r is the base radius and h is the height.
A = 2π(14)(33)
A = 924π
Since the barrel is open, there is only one circular base, which has an area of πr^2:
Base area = π(14^2)
Base area = 196π
Since there are two bases, the total area of the bases is twice the base area:
Total base area = 2(196π)
Total base area = 392π
Therefore, the surface area of the barrel is the sum of the curved surface area and the total base area:
Surface area = 924π + 392π
Surface area = 1316π
So, the surface area of the barrel is 1316π square units.
To find the volume of the barrel, we use the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius of the base, and h is the height.
Given that the radius of the base is 14 and the height is 33, we substitute these values into the formula:
V = π(14^2)(33)
V = π(196)(33)
V = 6468π
Therefore, the volume of the barrel is 6468π units cubed.
To find the surface area of the barrel, we need to consider the curved surface area and the base.
The curved surface area of a cylinder can be calculated using the formula:
A = 2πrh
where A is the surface area and h is the height.
In this case, the curved surface area will be the surface area of the inner cylinder subtracted from the surface area of the outer cylinder since it's a hollow cylinder.
For the outer cylinder:
A_outer = 2π(14)(33)
A_outer = 924π
For the inner cylinder, since it's hollow, it will have the same height as the outer cylinder but a smaller radius. We'll assume the inner radius is r_inner.
A_inner = 2π(r_inner)(33)
To find r_inner, we know that the thickness of the barrel, which is equal to the difference between the outer radius and inner radius, is given as 2. Therefore,
r_inner = 14 - 2 = 12
A_inner = 2π(12)(33)
A_inner = 792π
Finally, the surface area of the barrel is given by:
A = A_outer - A_inner
A = 924π - 792π
A = 132π
Therefore, the surface area of the barrel is 132π units squared.