Question

the total surface area if cube is 384 cm^2, find volume

Answer 1

Answer:

TSA of cube =

$6 {a}^{2}$

384=6a^2

a^2=384/6=64

a=√64=8

volume of cube=

${a}^{ 3}$

8^3

=512cm^2

Answer 2

Answer:-

★ Given:-

• Total Surface Area of cube = 384cm²

★ To Find:-

• Volume of cube

★ Formula Used:-

• TSA of cube = 6a²

• Volume of cube = a³

Here;

▪TSA = Total surface area

▪a = Side of cube

★ Solution:-

➽ Finding side of cube:

Let the side of the cube be a

According to given conditions;

TSA of cube = 384cm²

Putting the formula of TSA in above equation,

➟ 6a² = 384cm²

Solving the equation,

➟ 6a² = 384

➟ a² = 384 ÷ 6

➟ a² = 64

➟ a = √64

➟ a = √8×8

➟ a = 8

∴ a = side = 8cm

➽ Finding volume of cube:

Volume of cube = a³

Putting the value of a in above formula,

Volume of cube

= 8³

= 8 × 8 × 8

= 64 × 8

= 512 cm³

∴ Volume of cube is 512 cm³