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The curved surface area of a right circular cylinder is 1056 cm2 and its height is 16 cm. Find the total surface area of the cylinder. (Use π=722)
1200 cm²
1500 cm²
1760 cm²
1800 cm²
1500 cm²
Since TSA = CSA + 2πr², calculate r from CSA first. Given CSA = 1056, calculate 2πr = 1056/16 = 66. Then TSA = 1056 + (66 * r) = 1056 + (66 * 10.5) = 1056 + 693 = 1749.
Curved Surface Area (CSA) of a cylinder = 1056 cm², height (h) = 16 cm, use π = 22/7.
CSA=2πrh, TSA=2πrh+2πr2
Since TSA = CSA + 2πr², calculate r from CSA first. Given CSA = 1056, calculate 2πr = 1056/16 = 66. Then TSA = 1056 + (66 * r) = 1056 + (66 * 10.5) = 1056 + 693 = 1749.
Students often calculate only the Curved Surface Area or the area of the two bases (2πr2) instead of adding them together for the Total Surface Area.
Calculate the radius (r)
Use the CSA formula: 1056=2×722×r×16. Solve for r by simplifying: 1056=7704×r.
r=7041056×7=10.5 cm
Calculate the area of two circular bases
The base area of one circle is πr2. For two bases: 2×722×10.5×10.5.
2×722×110.25=693 cm2
Calculate Total Surface Area (TSA)
Add the CSA and the area of the two bases: TSA=1056+693.
TSA=1749 cm2
B is correct because the sum of the curved surface area (1056 cm²) and the two circular base areas (693 cm²) results in a total surface area of 1749 cm².
This concept is foundational for 'Volume and Capacity' problems; always verify if the question asks for lateral, curved, or total surface area before calculating.
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