Question

If the difference between the radii of two galaxies is 10 cm and the difference between the two volumes is 8800 cubic cm, then the product of the two radii will be -??
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Answer 1

Correct question :

If the difference between the radii of two galaxies is 10 cm and the difference between the two volumes is 880 cubic cm, then the product of the two radii will be -??

Answer:

$\color{violet} \huge \tt \: 26 \frac{1}{3}$

Step-by-step explanation:

$\color{red} \huge \tt \: given :$

$\tt \: r_{1} + r_{2} = 10 \: \: \: \: \: ...(i)$

$\tt \: and \: \frac{4}{3} \pi r_{1} ^{3} + \frac{4}{3} \pi { r_{2} }^{3} = 880$

$⟶ \: \tt \frac{4}{3} \pi( { r_{1}}^{3} + { r_{2} }^{3} ) = 180$

$⟶ \tt \: {r_{1} }^{3} + { r_{2} }^{3} = \frac{880 \times 3 \times 7}{4 \times 22} = 210 \: \: \: \: ...(ii)$

Taking the cube of both the sides of equation (i) we, have

$\tt( { r_{1} + r_{2} )}^{3} = 100$

$\tt⟶ r_{1}^{2} + r_{2} ^{2} + 3 r_{1} r_{2}( r_{1} r_{ 2} ) = 1000$

$\tt⟶210 + 3 r_{1} r_{2} (10) = 1000$

$\tt⟶30 r_{1} r_{2} = 1000 - 210$

$\tt⟶30 r_{1} r_{2} =790$

$\tt⟶ r_{1} r_{2} = \frac{790}{30}$

$\tt \color{purple} \boxed{ \tt⟶ r_{1} r_{2} =26 \frac{1}{3} }$