Given Information :
- Surface area of cube = 54 sq. units
To find :
Calculation :
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
Option B is correct.
