Question

If r,h and l be the radius , height and slant height of a cone respectively, then express 'l' in terms of r and h.

(A) √h²–r²

(B) √2h²–r²

(C) √r²–h²

(D) √h²+ r²

if you don't know please don't answer, if anyone gives silly or irrevelent answers I will report them.
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Answer 1

Answer:

C

Step-by-step explanation:

Hope this Helps :))

Answer 2

Answer:

$\displaystyle{\boxed{\red{\sf\:l\:=\:\sqrt{h^2\:+\:r^2}}}}$

Option D)

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

For a cone, we have given that,

$\displaystyle{\bullet\:\sf\:r\:=\:radius}$

$\displaystyle{\bullet\:\sf\:h\:=\:height}$

$\displaystyle{\bullet\:\sf\:l\:=\:slant\:height}$

Now, we know that,

The height of a cone is its perpendicular height, radius is base and the slant height is hypotenuse for a right triangle formed.

$\displaystyle{\therefore\:\pink{\sf\:(\:Slant\:height\:)^2\:=\:(\:Radius\:)^2\:+\:(\:Height\:)^2}\sf\:\:\:-\:-\:-\:[\:Pythagoras\:theorem\:]}$

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

$\displaystyle{\implies\sf\:\sqrt{l^2}\:=\:\sqrt{\:(\:r^2\:+\:h^2\:)}}$

$\displaystyle{\implies\sf\:l\:=\:\sqrt{r^2\:+\:h^2}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:l\:=\:\sqrt{h^2\:+\:r^2}}}}}$

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Additional Information:

1. Cone:

Any three dimensional figure having two surfaces with base circular in shape is called as cone.

2. Examples of conical objects:

Conical tent, ice - cream cone, sharpened end of pencil, etc. are some examples of conical objects.

3. Important formulae related to cone:

A cone having height $\sf\:h$, slant height $\sf\:l$ and radius $\sf\:r$ has following formulae:

$\displaystyle{\pink{\sf\:1.\:Area\:of\:base\:=\:\pi\:r^{2}}}$

$\displaystyle{\green{\sf\:2.\:l^{2}\:=\:r^{2}\:+\:h^{2}}\sf\:\:\:\:or\:\:\:\green{\sf\:l\:=\:\sqrt{r^{2}\:+\:h^{2}}}}$

$\displaystyle{\blue{\sf\:3.\:Curved\:surface\:area\:=\:\pi\:r\:l}}$

$\displaystyle{\orange{\sf\:4.\:Total\:surface\:area\:=\:\pi\:r\:(\:r\:+\:l\:)}}$

$\displaystyle{\red{\sf\:5.\:Volume\:=\:\dfrac{1}{3}\:\pi\:r^{2}\:h}}$