The triplicate ratio of $4 : 7$ is _____

49 : 16

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64 : 243

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16 : 49

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\sqrt[3]{4} : \sqrt[3]{7}

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Solution

The correct option is D $64 : 243$
The triplicate ratio of $a : b$ is $a^{3} : b^{3}$
$∴$ The triplicate ratio of $4 : 7$ is $4^{3} : 7^{3} = 64 : 243$

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Similar questions

Factorization of $64 a^{3} - 343 b^{3}$ is:

0 \times 0 = 0, 1 \times 1 = 1 d i f f e r e n c e = 1 1 \times 1 = 1, 2 \times 2 = 4 d i f f e r e n c e = 3 2 \times 2 = 4, 3 \times 3 = 9 d i f f e r e n c e = 5 3 \times 3 = 9, 4 \times 4 = 16 d i f f e r e n c e = 7 4 \times 4 = 16, 5 \times 5 = 25 d i f f e r e n c e = 9 5 \times 5 = 25, 6 \times 6 = 36 d i f f e r e n c e = 11 6 \times 6 = 36, 7 \times 7 = 49 d i f f e r e n c e = 13 7 \times 7 = 49, 8 \times 8 = 64 d i f f e r e n c e = 15

The areas of two similar triangles are $49 c m^{2}$ and $64 c m^{2}$ respectively. The ratio of their corresponding sides is

$\frac{16 x^{4}}{49 y^{2}} + \frac{49 y^{4}}{16 x^{2}} + 2 x y = (\frac{4 x^{2}}{7 y} + \frac{7 y^{2}}{4 x})^{2}$

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