Question

- The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved Surtace area is (a) 60 pie cm2 (b) 65 pie cm2 (c) 30pie cm 2 (d) none of these *​

Answer 1

Given :

• The radius of the base of a cone is 5 cm.

• The height of the cone is 12 cm.

To find :

• The curved surface area =?

Step-by-step explanation :

Firstly we have to find the Slant height of the cone,

As We know that,

Slant height = l² = r² + h²

l = √ r² + h²

Substituting the values in the above formula, we get,

= √ 5² + 12²

= √25 + 144

= √169

= 13

Therefore, Slant height of the cone = 13 cm.

Now,

As We know that,

Curved Surface Area of cone = πrl

Substituting the values in the above formula, we get,

= π × 5 × 13

= π × 65

= 65π

Therefore, Curved Surface Area of cone = 65π cm².

Hence, Option b. 65π cm² is the correct option.

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \purple{Question:-}}}}}}$

▪ The radius of the base of a cone is 5 cm and its height is 12 cm . Its curved surface area is ???

${ \huge{ \bold{ \underline{ \underline{ \purple{Solution:-}}}}}}$

${ \bold{ \underline{ \blue{Given-}}}}$

▪ The dimensions of a cone are given as follows in the question...

• Radius of the base ( R ) = 5 cm

• height of the cone ( h ) = 12 cm

${ \bold{ \underline{ \blue{To \: find-}}}}$

▪ Curved Surface Area of the cone???

${ \bold{curved \: surface \: area \: (CSA) \: of \: cone}}$

${ \boxed{ \bold{ \red{ \: \: CSA = \pi \: r \: l \: \: }}}}$

where,

▪ r = radius of the base of the cone

▪ l = slant height of the cone

${ \bold{ \red{l = \sqrt{ {r}^{2} + {h}^{2} } }}}$

${ \bold{ \implies{l = \sqrt{ {5}^{2} + {12}^{2} }}}}$

${ \bold{ \implies{l = \sqrt{25 + 144}}}}$

${ \bold{ \implies{l = \sqrt{169}}}}$

${ \bold{ \implies{ \red{l = 13 \: cm}}}}$

now,

substituting the values of r and l in the formula for curved surface area.....

${ \bold{ CSA = \pi \: r \: l}}$

${ \bold{ \implies{CSA = \pi \: \times 5cm \times 13cm}}}$

${ \boxed{ \bold{ \implies{ \red{CSA \: = 65 \: \pi \: {cm}^{2} }}}}}$

therefore,

option ( b ) is correct ......