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If a right circular cone of height 24 cm has a volume of 1232 cm³, then the total surface area of the cone is (use \(\pi = \frac{22}{7}\)):

1. 806 cm²
2. 704 cm²
3. 904 cm²
4. 608 cm²

Correct answer: 704 cm²

Solution

Use \(V=\frac{1}{3}\pi r^2 h\) to find \(r\). With \(V=1232\) and \(h=24\), we get \(r=7\) cm. Then slant height \(l=\sqrt{r^2+h^2}=25\) cm, so total surface area \(=\pi r(l+r)=\frac{22}{7}\cdot 7\cdot(25+7)=704\text{ cm}^2\).

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