The height and radius of the cone of which the frustum is a part are h1 and r1 respectively- If h2 and r2 are the heights and radius of the smaller base of the frustum respectively and h 2- h 1-1- 2- then r 2- r 1 is equal toa 1- 3b 1- 2c 2- 1d 3- 1

Since, are similar triangles, i.e., In OAO'L=OVO'V⇒r1r2=h1h1 h2⇒h1 h2r1=h1r2 ⇒r1h1 r1h2=h1r2⇒r1h1 h1r2=r1h2⇒h1r1 r2=r1h2⇒r1 r2r1=h2h1⇒r1 r2r1=12⇒1 r2r1=12 ...

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Byju's Answer

Standard X

Mathematics

Surface Area of a Frustum

The height an...

Question

The height and radius of the cone of which the frustum is a part are h₁ and r₁ respectively. If h₂ and r₂ are the heights and radius of the smaller base of the frustum respectively and h₂ : h₁ = 1 : 2, then r₂ : r₁ is equal to

(a) 1 : 3

(b) 1 : 2

(c) 2 : 1

(d) 3 : 1

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Solution

Since,

are similar triangles,

i.e., In

$\frac{O A}{O' L} = \frac{O V}{O' V} \Rightarrow \frac{r_{1}}{r_{2}} = \frac{h_{1}}{h_{1} - h_{2}} \Rightarrow (h_{1} - h_{2}) r_{1} = h_{1} r_{2}$
$\Rightarrow r_{1} h_{1} - r_{1} h_{2} = h_{1} r_{2} \Rightarrow r_{1} h_{1} - h_{1} r_{2} = r_{1} h_{2} \Rightarrow h_{1} (r_{1} - r_{2}) = r_{1} h_{2} \Rightarrow \frac{(r_{1} - r_{2})}{r_{1}} = \frac{h_{2}}{h_{1}} \Rightarrow \frac{(r_{1} - r_{2})}{r_{1}} = \frac{1}{2} \Rightarrow 1 - \frac{r_{2}}{r_{1}} = \frac{1}{2} \Rightarrow \frac{r_{2}}{r_{1}} = 1 - \frac{1}{2} = \frac{1}{2}$

Thus, $r_{2} : r_{1} = 1 : 2$

Hence, the correct answer is choice (b).

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