Question

the total surface area of a closed cone is 176 CM square if its radius is 4 cm find its slant
height​

Answer 1

S O L U T I O N :

Given,

• Total surface area of a closed cone is 176 cm².

• Radius (r) of a closed cone is 4 cm.

To Find,

• The slant height (l) of a closed cone.

Explanation,

We know that,

Total surface area of a cone = πr(l + r)

[ Put the values ]

=> 176 = 3.14 × 4 (l + 4)

=> 176 = 12.56(l + 4)

=> 176 = 12.56l + 50.24

=> 176 - 50.24 = 12.56l

=> 125.76 = 12.56l

=> l = 125.76/12.56

=> l = 10 cm

Therefore,

The slant height of a closed cone is 10 cm.

Answer 2

Given :-

Radius of cone the cone is 4 cm

Curved surface area of the cone is 176 cm²

To Prove:-

Slant height of the cone.

Solution:-

We know that ,

Using formula,

${ \underline{ \boxed{ \sf{Curved \: surface \: area \: = \pi rl}}}}$

$\\ \sf \: \pi rl \: = 176$

$\\ \sf \: 3.14 \times 4 \times l = 176$

$\\ \sf \: 12.56\times l + 4= 176$

$\\ \sf \: l \: = \frac{176}{16.56}$

$\\{ \underline{ \boxed{ \sf{l \: = 10.62 \: cm\:\:\:approx \:10\:cm}}}}$

Hence, the slant height of the cone is 10 cm.