Question

The height of a cone is 16 cm and its base radius is 12 cm. Find curved surface area and the total surface area of the cone​

Answer 1

first we need to find slant height of cone(l)

l^2= r^2+h^2

l^2= 144+256

l^2=400

l=20

NOW, curved surface area of cone=22/7×12×20

=754.287 sq.units

NOW, total surface area=754.287+22/7×144

=1206.8584 sq.units

Answer 2

Step-by-step explanation:

Given :-

• height of cone = 16 cm
• radius of cone = 12 cm

To find :-

• curved surface of cone
• total surface area of cone

$\color{red}\mathbb{We \: \: know \: \: that} \dashrightarrow$

$slant \: \: height, l = \sqrt{ {h}^{2} + {r}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \sqrt{ {16}^{2} + {12}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \sqrt{ 256 + 144}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \sqrt{400}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: 20 \: cm$

Now, Curved surface area of cone

$\implies \: \pi rl$

$\implies \: \frac{22}{7} \times 12 \times 20$

$\boxed{ \implies \frac{</em><em>5</em><em>2</em><em>8</em><em>0</em><em>}{7} \: cm}$

Now total surface area of cone

$\implies \: 2\pi r(r + l)$

$\implies \: 2 \times \frac{22}{7} \times12(12 + 20)$

$\implies2 \times \frac{22}{7} \times 264$

$\boxed{ \implies \: \frac{11616}{7} \: cm}$