Question

The curved surface area of a cone is 550 cm square diameter is 14 cm what is height?

Answer 1

CSA of a cone = πrl = 550

Radius = Diameter/2 = 14/2 = 7

550 = $\frac{22}{7}$ *7*l

⇒l = $\frac{550}{22}$

⇒l = 25

l² = h² + r²

⇒25² = h² + 7²

⇒h² = 625 - 49

⇒h² = 576

⇒h = $\sqrt{576}$

⇒Height = 24cm

Answer 2

AnswEr:-

Height of Cone is 24 cm.

Step by Step Explanation:-

Given:-

• Curved surface area of cone= 550 cm
• Diameter = 14cm

$\rule{150}2$

We know that,

Curved surface area of cone = πrl.

$\rule{150}2$

Now,

★ Putting Values:-

$:\implies\sf\; 550 cm^2\; =\; \dfrac{22}{7}\times\;7\times\; l$

$:\implies\sf\dfrac{550\times\;7}{22\times\;7} \; =\; l$

$:\implies\sf \; 25 cm = l$

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

$:\implies\sf\;25^2\;=\;7^2\;+\;h^2$

$:\implies\sf\;625\;=\;49\;+\;h^2$

$:\implies\sf\;625\;=\; h^2$

$:\implies\sf\;576\;=\;h^2$

$:\implies\sf\sqrt{576}\;=\; h$

$:\implies\large\boxed{\sf{\red{24cm = h}}}$

So, The Height of the Cone is 24cm.

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