Find the volume and the surface of the barrel with base radius 14 and a height of 33
To find the volume of a barrel, we can use the formula:
Volume = π * r^2 * h
where r is the base radius and h is the height.
Given that the base radius is 14 and the height is 33, we can substitute these values into the formula:
Volume = π * 14^2 * 33
= π * 196 * 33
= 20484π
So, the volume of the barrel is 20,484π cubic units.
To find the surface area of the barrel, we can break it down into three parts: the curved surface area, the top and bottom circles.
The curved surface area can be calculated using the formula:
Curved Surface Area = 2π * r * h
Given that the base radius is 14 and the height is 33, we can substitute these values into the formula:
Curved Surface Area = 2π * 14 * 33
= 924π
The surface area of the top and bottom circles can be calculated using the formula:
Circle Area = π * r^2
Given that the base radius is 14, we can substitute this value into the formula:
Circle Area = π * 14^2
= 196π
Since there are two circles (top and bottom), we multiply the circle area by 2:
Surface Area of the top and bottom circles = 2 * 196π
= 392π
The total surface area of the barrel is the sum of the curved surface area and the surface area of the top and bottom circles:
Surface Area = Curved Surface Area + Surface Area of the top and bottom circles
= 924π + 392π
= 1316π
So, the surface area of the barrel is 1316π square units.
To find the volume of the barrel, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
where r is the radius of the base and h is the height of the cylinder.
Substituting the values given, we have:
Volume = π * 14^2 * 33
Volume ≈ 19404π
So the volume of the barrel is approximately 19404π cubic units.
To find the surface area of the barrel, we need to consider the curved surface area and the circular top and bottom.
The formula for the curved surface area of a cylinder is:
Curved Surface Area = 2 * π * r * h
Substituting the values given, we have:
Curved Surface Area = 2 * π * 14 * 33
Curved Surface Area ≈ 2904π
The formula for the circular top and bottom of the barrel is:
Circular Area = 2 * π * r^2
Substituting the values, we have:
Circular Area = 2 * π * 14^2
Circular Area = 392π
Therefore, the total surface area of the barrel is:
Surface Area = Curved Surface Area + Circular Area
Surface Area ≈ 2904π + 392π
Surface Area ≈ 3296π
So the surface area of the barrel is approximately 3296π square units.