If the volume of two cubes are in the ratio of 27 : 64, then the ratio of their total surface area is

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RRB GG Exam (Bhopal) 2009 click here to view all questions

If the volume of two cubes are in the ratio of 27 : 64, then the ratio of their total surface area is

A27 : 64

B3 : 4

C9 : 16

D3 : 8

prasad ? Dec 20 '2019 at 17:9

Correct answer is:  9 : 16

Explanation:

\(\Large \frac{(a_{1})^{3}}{(a_{2})^{3}}=\frac{27}{64}\)

\(\Large \frac{a_{1}}{a_{2}}=\frac{3}{4}\)

Ratio of their total surface area

\(\Large =\frac{6a_{1}^{2}}{6a_{2}^{2}}= \left(\frac{a_{1}}{a_{2}}\right)^{2}\)

\(\Large = \left(\frac{3}{4}\right)^{2}=\frac{9}{16}=9:16\)

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Correct answer is:  9 : 16 Explanation: \(\Large \frac{(a_{1})^{3}}{(a_{2})^{3}}=\frac{27}{64}\) \(\Large \frac{a_{1}}{a_{2}}=\frac{3}{4}\) Ratio of their total surface area \(\Large =\frac{6a_{1}^{2}}{6a_{2}^{2}}= \left(\frac{a_{1}}{a_{2}}\right)^{2}\) \(\Large = \left(\frac{3}{4}\right)^{2}=\frac{9}{16}=9:16\) prasad ? answered Dec 20 '2019 at 17:9 All Comments

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