the surface area of a cylinder with a radius of 21 cm and a height of 42 cm. Use 22/7 for pi
.
Surface area = 2 (22/7) r^2 + 2 (22/7) r h.
Insert values and solve.
SA = 2(pi * r^2) + 2(pi * h)
SA = 2[(22/7 * 21^2)] + 2[(22/7) * 42)]
http://math.about.com/od/formulas/ss/surfaceareavol_3.htm
SA = 2(pi * r^2) + 2(pi * r * h)
SA = 2[(22/7 * 21^2)] + 2[(22/7) * 21 * 42)]
To find the surface area of a cylinder, we need to calculate the sum of the areas of the curved surface and the two circular bases.
1. Curved Surface Area of a Cylinder:
The curved surface area (CSA) of a cylinder can be found using the formula:
CSA = 2 * π * r * h
where π is approximately 22/7, r is the radius, and h is the height.
Substituting the given values:
CSA = 2 * (22/7) * 21 cm * 42 cm
CSA = 2 * 22 * 21 cm
2. Base Area of a Cylinder:
The base area (BA) of a cylinder is simply the area of one circular base, and can be found using the formula:
BA = π * r^2
where π is approximately 22/7 and r is the radius.
Substituting the given values:
BA = (22/7) * (21 cm)^2
BA = (22/7) * 441 cm^2
3. Total Surface Area of the Cylinder:
The total surface area (TSA) of a cylinder can be calculated by adding the curved surface area and the two base areas.
TSA = CSA + 2 * BA
Substituting the values:
TSA = (2 * 22 * 21 cm) + (2 * (22/7) * 441 cm^2)
Now, let's calculate the values:
CSA = 2 * 22 * 21 cm = 924 cm^2
BA = (22/7) * (21 cm)^2 = 1386 cm^2
TSA = (2 * 22 * 21 cm) + (2 * (22/7) * 441 cm^2)
TSA = 1848 cm^2 + 2772 cm^2
TSA = 4620 cm^2
Therefore, the surface area of the cylinder with a radius of 21 cm and a height of 42 cm is 4620 cm^2.