Question

The volumes of two spheres are in the ratio 64:27. The ratio of their diameter is:
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Answer 1

Answer:

$\red { Ratio \: of \: Diameter } \green { = 4:3}$

Step-by-step explanation:

$Let \: R \:and \: r \: are \: the \: radii\: of \: two\\Spheres$

$Ratio \: of \: volumes \: of \: two \: spheres = 64:27$

$\implies \left ( \frac{\frac{4}{3}\: R^{3}}{\frac{4}{3}\: r^{3}}\right)= \frac{4^{3}}{3^{3}}$

$\implies \frac{R^{3}}{r^{3}} = \frac{4^{3}}{3^{3}}$

$\implies \left( \frac{R}{r}\right )^{3}= \left( \frac{4}{3}\right)^{3}$

$\implies \frac{R}{r} = \frac{4}{3}$

$\frac{2R}{2r} = \frac{4}{3}$

$\implies \frac{D}{d} = \frac{4}{3}$

$Where \: \blue {D} \: and \: \orange {d} \: are \\diameters \: of \: two \: spheres \: respectively$

Therefore.,

$\red { Ratio \: of \: Diameter } \green { = 4:3}$

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Answer 2

Answer:

4:3

Step-by-step explanation:

Given ratio=64:27

We know that volume of a sphere= (4/3)×π×r^3

let volume of 1st sphere= (4/3)×π×(r)^3

and volume of 2nd sphere= (4/3)×π×(R)^3

volume of 1st sphere:volume of second sphere=64/27

=>(4/3)×π×(r)^3:(4/3×π×(R)^3=4^3:3^3

=>r^3:R^3=4^3:3^3

=>r:R=4:3

=>2r/2R=4/3

=>d/D=4/3

=>d:D=4:3