If the ratio of the radius to the height of a cylinder is 7:6 and the curved surface area of the cylinder is 1056 cm², then find the total surface area of the cylinder.

2218 cm²
2228 cm²
2248 cm²
2288 cm²

Correct answer: 2288 cm²

Solution

Given \(r:h=7:6\), let \(r=7k\) and \(h=6k\). From curved surface area, \(2\pi rh=1056\Rightarrow 84\pi k^2=1056\), which gives \(k=2\) using \(\pi=22/7\). Thus \(r=14\) cm and \(h=12\) cm, so total surface area is \(2\pi r(r+h)=2\pi\cdot14\cdot26=2288\) cm².

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