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Curved surface area of a cone. is $308 {cm}^{2}$ its slant height is 14 cm.

Find

(i) radius of the base and
(ii) total surface area of the cone

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8 cm and 461 {cm}^{2}

7 cm and 462 {cm}^{2}

3 cm and 463 {cm}^{2}

4 cm and 464 {cm}^{2}

answer is B.

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Detailed Solution

Given the cone curved surface area

CSA = 308 {cm}^{2}

and slant height

l = 14 cm

Suppose radius of the cone is r.
Cone's curved surface area

CSA = πrl

308 = \frac{22}{7} \times r \times 14

r =

\frac{(308 \times 7)}{(22 \times 14)}

r = 7 cm

Now, total surface area of the cone

= πr (r + 1)

= (\frac{22}{7} \times 7) (7 + 14)

= 22 \times 21

= 462 {cm}^{2}

Therefore,
Radius of base of cone =7 cm
Total surface area

= 462 {cm}^{2}

Option 2 is correct.

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