A cube has a surface are of 54. What's the volume?


A. 36

B. 27

C. 18

D. 64
80 points!!

We know that,

[tex]\bigstar \: \boxed{\sf {Volume_{(Cube)} = (\ell)^3}} \\ [/tex]

Let's find out the side first. We know that,

[tex]\bigstar \: \boxed{\sf {T.S.A_{(Cube)} = 6\ell^2}} \\ [/tex]

According to the question,

[tex] \longmapsto \sf {54 = 6\ell^2 } [/tex]

[tex] \longmapsto \sf {\dfrac{54}{6} = \ell^2 } [/tex]

[tex] \longmapsto \sf {9 = \ell^2 } [/tex]

[tex] \longmapsto \sf {\sqrt{9} = \ell } [/tex]

[tex] \longmapsto \sf \red{3 \: units = \ell } [/tex]

Now, calculating volume :

[tex]\bigstar \: \boxed{\sf {Volume_{(Cube)} = (\ell)^3}} \\ [/tex]

→ Volume = l × l × l

→ Volume = 3 × 3 × 3

→ Volume = 27

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