What is the total surface area of a cylinder with a radius of 4 cm and height of 6 cm
To find the total surface area of the cylinder, you need to add the areas of the two bases and the lateral surface area.
The formula for the lateral surface area of a cylinder is:
Lateral Surface Area = 2πrh
Where:
π (pi) is a constant approximately equal to 3.14159
r is the radius of the cylinder
h is the height of the cylinder
Given:
r = 4 cm
h = 6 cm
Lateral Surface Area = 2π(4)(6)
Lateral Surface Area = 48π
Lateral Surface Area ≈ 150.796 square cm
The formula for the area of a circle (base of the cylinder) is:
Area = πr^2
Base Area = π(4)^2
Base Area = 16π
Base Area ≈ 50.265 square cm
Now, to find the total surface area, add the areas of the two bases and the lateral surface area:
Total Surface Area = 2(Base Area) + Lateral Surface Area
Total Surface Area = 2(50.265) + 150.796
Total Surface Area = 100.53 + 150.796
Total Surface Area ≈ 251.326 square cm
Therefore, the total surface area of a cylinder with a radius of 4 cm and height of 6 cm is approximately 251.326 square cm.