Question

curved surface area of the cone is 308 cm^2 and it's slant height is 14 cm ^2 .find (i) radius of the base and ( ii) total surface area of the cone.

Answer 1

$\large{\boxed{\bold{Solution:}}}$

Given:


Curved surface area of cone = 308cm^2

it's slant height = 14 cm

Now,

Curved surface area of cone = 308 cm^2

=> πrl = 308cm^2

=> $\frac{22}{7} \times r \times 14 = 308 \: cm {}^{2}$

=> 44 r = 308 cm^2

=> r = $\frac{308}{44}$

=> r = 7 cm

Therefore, $\textbf{ the radius of base = 7 cm}$

Again, we know that

$\bold{total \: surface \: area = \pi \: r(l + r)}$

=> T.S.A = πr ( l + r )

=> T.S.A = $\frac{22}{7} \times 7(14 + 7)$

=> T.S.A = 22 × 21

=> T.S.A = 462 cm^2

Therefore,

$\bold{total \: surface \: area = 462 \: cm {}^{2} }$

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