Question

the curved surface area of a cone of radius 8 cm is 352 cm^2. find its height.​

Answer 1

Given: curved surface area of cone is 352cm² with radius of 8cm.

To Find: the height of cone(h) = ?

Formula:

$\bf \boxed{ \bf \: curved \: surface \: area \: of \: cone = \pi \: rl}$

Here,

• π = 22/7
• r = radius
• l = slant height

Solution

$\sf \implies \: \: \: \: \:352 {}^{2} = \pi \: rl$

$\sf \implies \: \: \: \: \: 352cm {}^{2} = \dfrac{22}{7} \times 8cm \times l$

$\sf \implies \: \: \: \: \: \dfrac{2464}{22} = 8l$

$\sf \implies \: \: \: \: \: 112 = 8l \: cm$

$\sf \implies \: \: \: \: \: l = \dfrac{112}{8}$

$\sf \implies \: \: \: \: \: \boxed{ \bf{l = 14cm}}$

By Pythagoras theorem,

(Slant height)² = (height)² + (radius)²

$\tt \: height = \sqrt{(14) {}^{2} - (8) {}^{2} }$

$\tt \: height = \sqrt{196 - 64}$

$\tt \: height = \sqrt{132}$

$\tt \: \implies\boxed{ \purple{ \bf{height = 11.4cm}}}$

$\bf\therefore \underline{height \: of \: cone\: is \: 11.4cm}.$

Answer 2

Height = 11.4cm

Given :-

• CSA of a Cone = 352cm²
• Radius of a Cone = 8cm

To Find :-

• Height of the cone

Solution :-

As we know that,

CSA of cone = πrl

=> 352 = 3.14 × 8 × l

=> 352 = 25.12 × l

=> l = 352/25.12

=> l = 14cm.

Applying Pythagoras theorem in Cone.

(Slant height)² = (Radius)² + (Height) ²

=> 14² = 8² + Height²

=> 296 = 64 + Height²

=> 296 - 64 = Height²

=> 132 = Height²

=> Height = √132

=> Height = 11.4cm.

Thus, the height of cone is 11.4cm.