If $C_{1}$ is a right circular cone with base radius $r_{1} c m$ and height $h_{1} c m$ and $C_{2}$ is a right circular cylinder with base radius $r_{2} c m$ and height $h_{2} c m$ ; and if $r_{1} : r_{2} = 1 : n$ (where $n$ is a positive integer) and their volumes are equal, then which one of the following is correct?

h_{1} = 3 n h_{2}

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h_{1} = 3 n^{2} h_{2}

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h_{1} = 3 h_{2}

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h_{1} = n^{2} h_{2}

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Solution

The correct option is B $h_{1} = 3 n^{2} h_{2}$
$C_{1} = \frac{π}{3} r_{1}^{2} h_{1}$
$C_{2} = π r_{2}^{2} h_{2}$
$C_{1} = C_{2} \Rightarrow r_{1}^{2} h_{1} = 3 r_{1}^{2} h_{2}$
$\Rightarrow h_{1} = 3 n^{2} h^{2}$

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Q. 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

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(b) 1 : 2

(c) 2 : 1

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What will be the area A of the quadrilateral in each case with their diagonal $d c m$ & the sum of their heights $(h_{1} + h_{2}) c m$ .

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ii) $d = 15, (h_{1} + h_{2}) = 20$

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iv) $d = 40, (h_{1} + h_{2}) = 30$

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If C1 is a right circular cone with base radius r1cm and height h1cm and C2 is a right circular cylinder with base radius r2cm and height h2cm; and if r1:r2=1:n (where n is a positive integer) and their volumes are equal, then which one of the following is correct?

The correct option is B h1=3n2h2C1=π3r21h1C2=πr22h2C1=C2⇒r21h1=3r21h2⇒h1=3n2h2

The correct option is B $h_{1} = 3 n^{2} h_{2}$
$C_{1} = \frac{π}{3} r_{1}^{2} h_{1}$
$C_{2} = π r_{2}^{2} h_{2}$
$C_{1} = C_{2} \Rightarrow r_{1}^{2} h_{1} = 3 r_{1}^{2} h_{2}$
$\Rightarrow h_{1} = 3 n^{2} h^{2}$