The curved surface area of a cylinder of height 14 cm is 88 cm². The diameter of its circular base is
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Explanation:
The curved surface area (CSA) of a cylinder is given by the formula:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the height of the cylinder.
From the problem, the CSA is 88 cm² and the height (h) is 14 cm. Substituting these values into the formula:
88 = 2πr(14).
Simplify:
88 = 28πr.
Divide both sides by 28π to isolate r:
r = 88 / (28π).
Using π ≈ 22/7 for calculation:
r = 88 / (28 × 22/7),
r = 88 / (4 × 22),
r = 88 / 88,
r = 1 cm.
The diameter (d) of the circular base is twice the radius:
d = 2r = 2 × 1 = 2 cm.
Thus, the diameter of the circular base is 2 cm, which corresponds to option d) 2 cm.