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A cylinder has a radius of 7 cm and a height of 10 cm. What is the total surface area of the cylinder?
658 cm┬▓
748 cm┬▓
528 cm┬▓
880 cm┬▓
748 cm┬▓
Since the radius is 7, use the approximation ╧А=722тАЛ. The formula simplifies to 2├Ч22├Ч(7+10)=44├Ч17. Calculate 44├Ч10=440 and 44├Ч7=308; summing these gives 748.
Radius of the cylinder (r) = 7 cm, Height of the cylinder (h) = 10 cm.
TSA=2╧Аr(r+h)
Since the radius is 7, use the approximation ╧А=722тАЛ. The formula simplifies to 2├Ч22├Ч(7+10)=44├Ч17. Calculate 44├Ч10=440 and 44├Ч7=308; summing these gives 748.
Many students calculate only the lateral surface area (2╧Аrh) and forget to add the areas of the two circular bases (2╧Аr2).
State the formula
The total surface area (TSA) of a cylinder includes the lateral surface area and the area of the top and bottom circular bases.
TSA=2╧Аrh+2╧Аr2=2╧Аr(r+h)
Substitute the given values
Plug in the values r=7 and h=10 into the formula, using ╧А=722тАЛ.
TSA=2├Ч722тАЛ├Ч7├Ч(7+10)
Perform the calculation
Cancel the 7 in the numerator and denominator, then multiply the remaining terms.
TSA=2├Ч22├Ч17=44├Ч17=748
B is correct because the calculated total surface area is 748 cm┬▓.
Always verify if the question asks for 'Lateral Surface Area' (curved part only) or 'Total Surface Area' (including bases) as this is a frequent differentiator in competitive geometry problems.