Question

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14. Volume of a solid cubical box whose surface area is 600 cm'is
a. 1600 cm3
b. 1000 cm3
c. 900 cm3

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Answer 1

Given:

• The surface area of a cubical box is 600cm

To Find:

• The volume of the cubical box

Solution:

➢ Now over here we've got the surface are of the cube and we have to find the volume of it.?

➢ so, now we base up the surface area of the cube to find the side of the cube and then find its volume.

$\underline \mathfrak{As \: we \: know \: that \dag}$

$\pink{ \underline{ \boxed {\sf{sufacre \: area \: of \: a \: cube = 6( {side}^{2} )}}}} \pink\bigstar$

${ : \implies} \sf\: 600 {cm}^{2} = 6 \times ( {side}^{2} ) \\ \\ \\ { : \implies} \sf {side}^{2} = \cancel \frac{600}{6} {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: {side}^{2} = 100 {cm}^{2} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: side = \sqrt{100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \longrightarrow} \bf \: side = \orange{ 10cm \bigstar} \: \: \: \: \: \: \:$

$\therefore \purple{\underline{ \rm{ the \: side \: of \: the \: cube \: is \: 10cm ^{ \bigstar} }}}$

➢since ,we found the side let's find the volume of the cube

$\underline \mathfrak{As \: we \: know \: that \dag}$

$\pink{ \underline{ \boxed{ \sf{ \: volume \: of \: a \: cube \: is \: side \times side \times side}}}}$

${ : \implies} \sf \: volue \: of \: the \: cube \: = side ^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: volume \: of \: the \: cube = {10}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \pink {\underline{ \boxed{ \sf{ \therefore \: the \: volume \: of \: the \: cube = 1000 {cm}^{3} }}} \bigstar}$

More to know:

$\leadsto \sf volume \: of \: cubiod = l \times b \times h \: \: \: \: \: \: \: \\ \\ \leadsto \sf \: l.s.a \: of \: cube = 4( {side}^{2} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \leadsto \sf \: t.s.a \: of \: cubiod = 2(lb + bh + hl) \\ \\ \leadsto \sf \: l.s.a \: of \: cboid = 2h(l + b) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Answer 2

Given :-

• Shape = Cube
• Total Surface Area of Cube = 600cm²

To Find :-

• Volume of the Cube.

Solution :-

➞ Total Surface Area of Cube = 6(side)²

➞ 600 = 6 × (side)²

➞ 600 ÷ 6 = (side)²

➞ 100 = (side)²

➞ √100 = side

➞ 10cm = side

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➞ Volume of Cube = (side)³

➞ Volume of Cube = side × side × side

➞ Volume of Cube = 10 × 10 × 10

➞ Volume of Cube = 100 × 10

➞ Volume of Cube = 1000cm³

Therefore, Correct Option is B i.e 1000cm³

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★ Additional Info :

Formulas Related to Cube :

• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³

Where a stands for Side

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