Question

Three solid metallic sphere of radii 3cm,4cm,5cm respectively are melted to form a single solid sphere . Find the diameter of the sphere

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Diameter of the single solid sphere (D)= 12 cm

Step-by-step explanation:

$Let\: r_{1}, r_{2} \:and \: r_{3}\:are \: radii\\of \: three \: metallic \: spears$

$It \: is \: given \: that \\ r_{1}= 3\:cm , \: r_{2}= 4\:cm , \: r_{3}= 5\:cm$

/* According to the problem given,

Three solid spears melted to form a single solid sphere

Let single spear radius = R cm

$\boxed { Volume \: of \: a \: sphere (V) = \frac{4}{3} \pi (radius)^{3}}$

$\implies \frac{4}{3} \pi r_{1}^{3}+\frac{4}{3} \pi r_{2}^{3}+\frac{4}{3} \pi r_{3}^{3} = \frac{4}{3} \pi R^{3}$

$\implies \frac{4}{3} \pi ( r_{1}^{3}+r_{2}^{3}+r_{3}^{3})=\frac{4}{3} \pi R^{3}$

$\implies r_{1}^{3}+r_{2}^{3}+r_{3}^{3}= R^{3}$

$\implies 3^{3}+4^{3}+5^{3}=R^{3}$

$\implies 27 + 64 + 125 = R^{3}$

$\implies 216 = R^{3}$

$\implies R = \sqrt[3]{216}$

$\implies R = \sqrt[3]{6^{3}}$

$\implies R = 6 \: cm$

Therefore,

Diameter of the single solid sphere (D) = 2R

Diameter of the single solid sphere (D) = 2R= 2 × 6 cm

Diameter of the single solid sphere (D) = 2R= 2 × 6 cm= 12 cm

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