Question

find the volume of a cube whose total surface area is 384 cm².​

Answer 1

Answer: V = 512

Step-by-step explanation:

Answer 2

$\huge \maltese \: \sf{ \pink{ Question:- }}$

• Find the volume of a cube whose total surface area is 384 cm².

$\huge{ \underline{ \underline{ \sf{Given:- }}}}$

• Surface area of cube is 384 cm².

$\huge \sf{ \underline{ \underline{To \: find:-}}}$

• The volume of cube

$\huge \pink{ \underline{ \underline{ \sf{{Solution:- }}}}}$

• We will first find the sides of the cubes

$\sf \: Surface \: area \: of \: cube = 6 {a}^{2}$

$\longrightarrow \: 6 {a}^{2} = 384$

$\longrightarrow \: {a}^{2} = \frac{348}{6}$

$\longrightarrow \: {a}^{2} = 64$

$\longrightarrow \: {a} = \sqrt{64}$

$a = 8$

$\bf \therefore \: the \: measures \: of \: sides \: of \: the \: cube \: is \: 8 cm.$

Volume of cube=a³

⇒volume= 8³

⇒ 512cm³

$\boxed{\therefore \bf \: the \: volume \: of \: cube \: is \: \boxed{ \mathfrak{ \green{ 64 {cm}^{3} }}}}$

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Learn more volume related formulas:-

• Volume of cylinder =π²h
• Volume of cube= a³
• Volume of cuboid = length ×breadth ×height
• Volume of cone= ⅓πr²h