Find the surface area of a cylinder with the given dimensions. Round to the nearest tenth.
d= 14mm and H = 32mm
https://www.google.com/search?source=hp&ei=oDnaWvXWJsHGsAWRw6eIBw&q=surface+area+of+a+cylinder&oq=+surface+area+of+a+cylinder&gs_l=psy-ab.1.0.35i39k1j0l9.3783.3783.0.7222.2.1.0.0.0.0.132.132.0j1.1.0....0...1c.1.64.psy-ab..1.1.131.0...0.MKgQq7ihdSw
To find the surface area of a cylinder, you need to calculate the areas of the two circular bases and the curved surface area.
1. Calculate the area of the circular bases:
The area of a circle can be found using the formula A = πr^2, where r is the radius.
In this case, the diameter, d, is given as 14mm. The radius, r, is half the diameter, so r = 14mm / 2 = 7mm.
Calculate the area of one circular base using the formula: A_base = πr^2.
A_base = π(7mm)^2
A_base = π(49mm^2)
A_base ≈ 153.94mm^2 (rounded to the nearest tenth)
Since there are two circular bases, multiply the area of one base by 2 to get the total area of the two bases.
Total base area = 2 * A_base ≈ 2 * 153.94mm^2 ≈ 307.88 mm^2
2. Calculate the curved surface area:
The curved surface area of a cylinder can be found using the formula A_curved = 2πrh, where r is the radius and h is the height of the cylinder.
In this case, the radius, r, is 7mm, and the height, H, is 32mm.
Calculate the curved surface area using the formula: A_curved = 2πrh.
A_curved = 2π(7mm)(32mm)
A_curved = 2π(224mm^2)
A_curved ≈ 1407.96mm^2 (rounded to the nearest tenth)
3. Calculate the total surface area:
The total surface area of the cylinder is the sum of the base area and the curved surface area.
Total surface area = Total base area + Curved surface area.
Total surface area ≈ 307.88mm^2 + 1407.96mm^2 ≈ 1715.84mm^2 (rounded to the nearest tenth)
Therefore, the surface area of the cylinder is approximately 1715.84 mm^2 (rounded to the nearest tenth).