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Question
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
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Solution
(i)
`("Edge")^3` = Volume of a cube
`("Edge")^3` = 216 cm3
⇒ Edge = `(216)^(1/3)`
⇒ Edge = `(3 xx 3 xx 3 xx 2 xx 2 xx 2)^(1/3)`
⇒ Edge = `3 xx 2`
⇒ Edge = 6 cm.
(ii)
`("Edge")^3` = Volume of a cube
`("Edge")^3` = 1.728 m3
⇒ `("Edge")^3 = 1.728/1.000 = 1728/1000`
⇒ Edge = `(1728/1000)^(1/3)`
⇒ Edge = `((2 xx 2xx 2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 3)/(10 xx 10 xx 10))^(1/3)`
⇒ Edge = `(2 xx 2 xx 3)/10`
⇒ Edge = `12/10`m
⇒ Edge = 1.2 m
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