Question

Example 1. The height of a cone is 16 cm and its base
radius is 12 cm. Find the curved surface area and the
total surface area of the cone. (take, = 314)

Answer 1

Given :

Height of the cone => 16cm

Radius of the cone => 12cm

π => 3.14

To Find :

Curved surface area (C.S.A)

Total surface area (T.S.A)

Solution :

We know curved surface area of the cone => πrl

Here,

Pi(π) => 3.14

Radius(r) => 12

Slant hieght(l) => ?

We know,

$\sf{}l^2=h^2+r^2$

So,

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

$\sf{}\implies l^2=256+144$

$\sf{}\implies l=400$

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

$\sf{}\therefore l=20$

Therefore,curved surface area of the cone :-

$\sf{}\sf{}C.S.A=\pi rl=3.14\times 12\times 20=753.6cm^2$

We know total surface area of the cone=> πr(r + l)

$\sf{}\implies 3.14\times 12(12+20)$

$\sf{}\implies 3.14 \times 12 \times 32$

$\sf{}\therefore 1205.76$

Thus,curved surface area of the given cone is 753.6cm^2 and total surface area is 1205.76cm^2

Answer 2

Step-by-step explanation:

π = 3.14

height of cone = 16cm

radius of cone = 12cm

let length of cone = x cm

• to find length formula used

L²=r²+h²

using above formula

x² = 16² + 12²

x = √(256+144)

x = 20 cm

length of cone = 20 cm

• total surface area of cone

πr(r+l)

using above formula total surface area of cone=

3.14×12cm(12cm+20cm)

→3.14×384cm²

→1205.76cm²

• curved surface area of cone

πrl

using above formula curved surface area of cone=

3.14×12 cm×20 cm

=753.6cm²

hence,

total surface area of cone=1205.76cm²

total surface area of cone=1205.76cm²curved surface area of cone=753.6cm²