Question

The radius and height of a cone are 7 and 24, then the lateral height of the cone is:

Answer 1

Answer:

24 m

Step-by-step explanation:

Here we use Pythagoras theorem

$h = \sqrt{ {p}^{2} + {b}^{2} } \\ lateral \: length(l) = \sqrt{ {7}^{2} + {24}^{2} } \\ l = \sqrt{49 + 576} \\ l = \sqrt{625} \\ l = 25$

Answer 2

Correct Question :

The radius and height of a cone are 7 cm and 24 cm , then what is the lateral height of the cone ?

Given :

• Radius of the cone(r) = 7 cm.
• Height of the cone(h) = 24 cm.

To find :

• Lateral height(l) of the cone.

Solution :

We know,

${\boxed{\bold{l^2=h^2+r^2}}}$

$\implies \sf \: {l}^{2} = {r}^{2} + {h}^{2} \\ \implies \sf \: {l}^{2} = {7}^{2} + {24}^{2} \\ \implies \sf \: {l}^{2} = 49 + 576 \\ \implies \sf \: {l}^{2} = 625 \\ \implies \sf \: l = \sqrt{625} \\ \implies \sf \: l = 25$

Therefore, lateral height of the cone is 25 cm.

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More information :

• T.S.A of cone = πr(r+l)

• C.S.A of cone = πrl

• Volume of cone = 1/3 πr²h

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