The slant height l of a cone of radius r and height h isA- -r2-hB- r 2- h 2C- - r 2- h 2D- r 2- h 22

Right Circular Cone and Its Surface Area

The slant hei...

Question

The slant height (l) of a cone of radius r and height h is

\sqrt{r^{2} + h}

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r^{2} + h^{2}

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\sqrt{r^{2} + h^{2}}

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(r^{2} + h^{2})^{2}

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Solution

The correct option is C $\sqrt{r^{2} + h^{2}}$

By observing the figure and by applying Pythagoras' theorem in the right-angles triangle whose base is r, height is h and hypotenuse is l(slant height of cone), we get
$l^{2} = r^{2} + h^{2}$
$\Rightarrow l = \sqrt{r^{2} + h^{2}}$

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The radii of the bases of two solid right circular cones of same height are $r_{1}$ and $r_{2}$ respectively. The cones are melted and recast into a solid sphere of radius R. Find the height of each cone in terms of $r_{1}, r_{2}$ and R.

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The slant height (l) of a cone of radius r and height h is

The correct option is C √r2+h2 By observing the figure and by applying Pythagoras' theorem in the right-angles triangle whose base is r, height is h and hypotenuse is l(slant height of cone), we get l2=r2+h2 ⇒l=√r2+h2

The correct option is C $\sqrt{r^{2} + h^{2}}$

By observing the figure and by applying Pythagoras' theorem in the right-angles triangle whose base is r, height is h and hypotenuse is l(slant height of cone), we get
$l^{2} = r^{2} + h^{2}$
$\Rightarrow l = \sqrt{r^{2} + h^{2}}$