Question : The area of the base of a cone is 616 cm2. If its slant height is 20 cm, then what is the total surface area of the cone? [Use $\pi$ = $\frac{22}{7}$]
Option 1: 1352 cm2
Option 2: 1296 cm2
Option 3: 1496 cm2
Option 4: 1524 cm2
Correct Answer: 1496 cm 2
Solution : Total Surface Area of a cone = Base Area + Curved Surface Area The base area is given as 616 cm 2 . The curved surface area of a cone = $\pi r l$, where $r$ is the radius of the base and $l$ is the slant height. Base Area = $\pi r^2$ $r = \sqrt{\frac{\text{Base Area}}{\pi}} = \sqrt{\frac{616}{\pi}}=\sqrt{196}= 14 \text{ cm}$ So, Curved Surface Area = $\pi \times 14 \times 20 = 880$ cm 2 $\therefore$ Total Surface Area = Base Area + Curved Surface Area = 616 + 880 = 1496 cm 2 Hence, the correct answer is 1496 cm 2 .
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