Question

vi) Area of whole surface of a cube is 216
sq. cm, then the volume of the cube is
a) 343 cu.cm.
(b) 216 cu.cm
c)
121 cu.cm.
(d) 225 cu.cm.
​

Answer 1

Explanation:

✬ Volume = 216 cm³ ✬

Step-by-step explanation:

Given:

Total surface area of cube is 216 cm².

To Find:

• What is the volume of cube ?

Solution: Let the side of cube be a cm.

As we know that

★ Total Surface Area of Cube = 6a² ★

A/q

TSA is 216 cm².

➼ 216 = 6 × a²

➼ 216/6 = a²

➼ √36 = a

➼ 6 cm = a

Now volume of cube will be

★ Volume of Cube = a³ cubic units ★

$\implies{\rm }⟹ Volume = 6³$

$\implies{\rm }⟹ (6 × 6 × 6) cm³$

$\implies{\rm }⟹ 216 cm³$

Hence, the volume of cube will be 216 cm³.

Answer 2

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As others have pointed out the volume (V) is 216 cm^3

A numeric value equal to the surface area (SA) of 216 cm^2.

So if we ignore the units,

V = SA in this specific case.

Let the length of one side be x.

x^3 = 6*x^2 … divide both sides by x^2

x = 6 is the only value where SA = V.

Option (b) 216³ cm is your answer...

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