Question

The height of a cone is 16 cm and it's base radius is 12 cm.
Find the curved surface area of the cone . ( Use 3.14 )

Answer 1

Answer:

Given :-

• The height of a cone is 16 cm and it's base radius is 12 cm.

To Find :-

• What is the curved surface area of the cone. (Use π = 3.14).

Formula Used :-

$\clubsuit$ Curved Surface Area or C.S.A Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{C.S.A_{(Cone)} =\: {\pi}rl}}}\: \: \: \bigstar$

where,

• C.S.A = Curved Surface Area
• π = Pie or 22/7
• l = Slant Height

Solution :-

First, we have to find the slant height of a cone :

Given :

• Height = 16 cm
• Radius = 12 cm

According to the question by using the formula we get,

$\footnotesize \implies \bf (Slant\: Height)^2 =\: (Height)^2 + (Radius)^2$

$\implies \sf (l)^2 =\: (h)^2 + (r)^2$

$\implies \sf (l)^2 =\: (16)^2 + (12)^2$

$\implies \sf (l)^2 =\: (16 \times 16) + (12 \times 12)$

$\implies \sf (l)^2 =\: 256 + 144$

$\implies \sf (l)^2 =\: 400$

$\implies \sf l =\: \sqrt{400}$

$\implies \sf\bold{\purple{l =\: 20\: cm}}$

Hence, the slant height is 20 cm .

Now, we have to find the curved surface area of the cone :

Given :

• Radius = 12 cm
• Slant Height = 20 cm

According to the question by using the formula we get,

$\implies \bf C.S.A_{(Cone)} =\: {\pi}rl$

$\implies \sf C.S.A_{(Cone)} =\: 3.14 \times 12 \times 20$

$\implies \sf\bold{\red{C.S.A_{(Cone)} =\: 753.6\: cm^2}}$

$\therefore$ The curved surface area of the cone is 753.6 cm² .