A cylinder has a diameter of 6 ft and a height of 3 ft. Find its surface area and volume.
Surface area: 2*PI*Diameter + height*PI*D
Volume: PI r^2 * height
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To find the surface area and volume of a cylinder, we can use the formulas:
Surface Area = 2πr² + 2πrh
Volume = πr²h
Where:
- r is the radius of the cylinder (half of the diameter)
- h is the height of the cylinder
- π (pi) is a mathematical constant approximately equal to 3.14159
Let's calculate the surface area and volume of the given cylinder:
1. Find the radius:
The diameter of the cylinder is 6 ft, which means the radius is half of that, so the radius (r) would be 6 ft / 2 = 3 ft.
2. Calculate the surface area using the formula:
Surface Area = 2πr² + 2πrh
Substituting the values:
Surface Area = 2π(3 ft)² + 2π(3 ft)(3 ft)
Surface Area = 2π(9 ft²) + 2π(9 ft²)
Surface Area = 18π ft² + 18π ft²
Surface Area = 36π ft²
So, the surface area of the cylinder is 36π ft².
3. Calculate the volume using the formula:
Volume = πr²h
Substituting the values:
Volume = π(3 ft)²(3 ft)
Volume = π(9 ft²)(3 ft)
Volume = 27π ft³
So, the volume of the cylinder is 27π ft³.