The radii of the ends of a frustum of a cone are r1 and r2 cm- If h cm is the height of the frustum then the height of the cone of which the frustum is a part-is

Let the height of the cone be H cm. Here, ∆OAB ∆OCD ∴OAOC=ABCD⇒H hH=r1r2⇒hH=1 r1r2 ⇒hH=r2 r1r2⇒H=r2r2 r1h The radii of the ends of a frustum of a cone ar ...

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Standard X

Mathematics

Surface Area of a Frustum

The radii of ...

Question

The radii of the ends of a frustum of a cone are r₁ and r₂ cm. If h cm is the height of the frustum then the height of the cone of which the frustum is a part, is ________.

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Solution

Let the height of the cone be H cm.

Here, ∆OAB ~ ∆OCD

$∴ \frac{OA}{OC} = \frac{AB}{CD} \Rightarrow \frac{H - h}{H} = \frac{r_{1}}{r_{2}} \Rightarrow \frac{h}{H} = 1 - \frac{r_{1}}{r_{2}}$
$\Rightarrow \frac{h}{H} = \frac{r_{2} - r_{1}}{r_{2}} \Rightarrow H = (\frac{r_{2}}{r_{2} - r_{1}}) h$

The radii of the ends of a frustum of a cone are r₁ and r₂ cm. If h cm is the height of the frustum then the height of the cone of which the frustum is a part, is $(\frac{r_{2}}{r_{2} - r_{1}}) h$ .

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The radii of the ends of a frustum of a cone are r1 and r2 cm. If h cm is the height of the frustum then the height of the cone of which the frustum is a part, is ________.

Let the height of the cone be H cm. Here, ∆OAB ~ ∆OCD ∴OAOC=ABCD⇒H-hH=r1r2⇒hH=1-r1r2 ⇒hH=r2-r1r2⇒H=r2r2-r1h The radii of the ends of a frustum of a cone are r1 and r2 cm. If h cm is the height of the frustum then the height of the cone of which the frustum is a part, is r2r2-r1h .

The radii of the ends of a frustum of a cone are r₁ and r₂ cm. If h cm is the height of the frustum then the height of the cone of which the frustum is a part, is ________.