Question

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is
(a)60π cm²
(b)68π cm²
(c)120π cm²
(d)136π cm²

Answer 1

Answer:

The Curved surface area of a cone is  136 π cm² .

Among the given options option (d) 136 π cm² is the correct answer.

Step-by-step explanation:

Given :  

Height of a right circular cone , h = 15 cm  

Diameter of a right circular cone = 16 cm

Radius  of a right circular cone , r = 16/2 = 8 cm

Slant height of the cone, l = √r² + h²

l = √8² + 15²

l = √64 + 225

l = √289

l = 17 cm

Slant height of the cone = 17 cm

Curved surface area of a cone,C. S.A = πrl

C. S.A = π × 8 × 17

C. S.A = 136 π cm ²

Curved surface area of a cone = 136 π cm²  

Hence , the Curved surface area of a cone is  136 π cm² .

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Answer 2

$\huge{\underline{\underline{\bold{\mathtt{Answer:}}}}}$

Option (D)136Π cm²

$\huge{\underline{\underline{\bold{\mathtt{Explanation:}}}}}$

Given,

diameter = 16 cm

Radius = 16/2 = 8cm

height = 15 cm

To find :

Curved surface area of a right circular cone = Π × r × L

Now we need to find "L"

As we know that,

$l = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ = \sqrt{ {15}^{2} + {8}^{2} } \\ \\ = \sqrt{225 + 64} \\ \\ = \sqrt{289} \\ \\ = 17$

We get L = 17cm

Curved surface area of a right circular cone = $= \frac{22}{7} \times 8 \times 17 = \\ \\ =136 \pi \\ \\ = 427.428$cm²

$\rule{200}{2}$

$\underline{\underline{\bold{\mathtt{Formula's\: used}}}}$:—

$\implies{\bold{\mathsf{(slant hieght)L = \sqrt{ {r}^{2} + {h}^{2} } }}}$

$\implies{\bold{\mathsf{CSA\: of\:Cone=\pi \times r \times L}}}$