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

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

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.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity