Question

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

A. 36

B. 27

C. 18

D. 64
80 points!!

Answer 1

Given Information :

• Surface area of cube = 54 sq. units

To find :

• Volume

Calculation :

We know that,

`\bigstar \: \boxed{\sf {Volume_((Cube)) = (\ell)^3}} \\`

• l = length of side

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

`\bigstar \: \boxed{\sf {T.S.A_((Cube)) = 6\ell^2}} \\`

According to the question,

`\longmapsto \sf {54 = 6\ell^2 }`

`\longmapsto \sf {(54)/(6) = \ell^2 }`

`\longmapsto \sf {9 = \ell^2 }`

`\longmapsto \sf {√(9) = \ell }`

`\longmapsto \sf \red{3 \: units = \ell }`

Now, calculating volume :

`\bigstar \: \boxed{\sf {Volume_((Cube)) = (\ell)^3}} \\`

→ Volume = l × l × l

→ Volume = 3 × 3 × 3

→ Volume = 27

Option B is correct.