Question
a barrel has a diameter of 12 inches and a height of ten inches what is the surface area in square inches of the barrel
Answers
GPT 3.5
To calculate the surface area of a barrel, we need to find the area of the curved surface, along with the area of the two circular bases.
The curved surface area of a cylinder can be calculated using the formula: A = 2πrh, where A represents the curved surface area, π is a constant approximately equal to 3.14, r is the radius of the barrel, and h is the height of the barrel.
Since the diameter is given as 12 inches, the radius would be half of that: r = 12/2 = 6 inches.
The height of the barrel is given as 10 inches: h = 10 inches.
By substituting the values into the formula, we have:
A = 2 * π * 6 * 10
A = 120π square inches
To find the area of each circular base, we can use the formula: A = πr^2, where r is the radius of the base.
The radius is 6 inches, so we have:
A = π * 6^2
A = 36π square inches
Since we have two bases, we need to multiply this area by 2.
Surface Area = Curved Surface Area + 2 * Base Area
Surface Area = 120π + 2 * (36π)
Surface Area = 120π + 72π
Surface Area = 192π square inches
Considering an approximate value for π = 3.14, the surface area of the barrel would be:
Surface Area ≈ 192 * 3.14
Surface Area ≈ 603.68 square inches
Therefore, the surface area of the barrel is approximately 603.68 square inches.
The curved surface area of a cylinder can be calculated using the formula: A = 2πrh, where A represents the curved surface area, π is a constant approximately equal to 3.14, r is the radius of the barrel, and h is the height of the barrel.
Since the diameter is given as 12 inches, the radius would be half of that: r = 12/2 = 6 inches.
The height of the barrel is given as 10 inches: h = 10 inches.
By substituting the values into the formula, we have:
A = 2 * π * 6 * 10
A = 120π square inches
To find the area of each circular base, we can use the formula: A = πr^2, where r is the radius of the base.
The radius is 6 inches, so we have:
A = π * 6^2
A = 36π square inches
Since we have two bases, we need to multiply this area by 2.
Surface Area = Curved Surface Area + 2 * Base Area
Surface Area = 120π + 2 * (36π)
Surface Area = 120π + 72π
Surface Area = 192π square inches
Considering an approximate value for π = 3.14, the surface area of the barrel would be:
Surface Area ≈ 192 * 3.14
Surface Area ≈ 603.68 square inches
Therefore, the surface area of the barrel is approximately 603.68 square inches.