Question

Q4. Volume of a cube whose
surface area is 486 sq. meter is
equal to
729 cu. meter
27 cu. meter
324 cu. meter
162 cu. meter​

Answer 1

GIVEN:

• Surface area of cube = 486 m²

TO FIND:

• What is the volume of cube ?

SOLUTION:

Let the side of the cube be 'x' m

We know that the formula for finding the Surface area of cube is:-

$\large{\boxed{\bf{\star \: TSA = 6(side)^2 \: \star}}}$

According to question:-

$\sf{\longmapsto 486 = 6(x)^2}$

$\sf{\longmapsto \cancel\dfrac{486}{6} = x^2 }$

$\sf{\longmapsto 81 = x^2 }$

$\sf{\longmapsto \sqrt{81} = x }$

$\bf{\longmapsto 9 \: m = x }$

• Side of cube = 9m

To find the volume of cube, we use the formula:-

$\large{\boxed{\bf{\star \: VOLUME = (side)^3 \: \star}}}$

According to question:-

$\sf{\longmapsto VOLUME = (9)^3 }$

$\sf{\longmapsto VOLUME = 9 \times 9 \times 9 }$

$\bf{\longmapsto VOLUME = 729 \: m^3 }$

❝ Hence, the volume of cube is 729 m³ ❞

______________________

Answer 2

Given ,

• Surface area of cube = 486 m²

We know that , the total surface area of cube is given by

$\large\boxed{ \sf{TSA \: of \: cube = 6 \times {(side)}^{2} }}$

Thus ,

486 = 6 × (side)²

(side)² = 81

side = √81

side = 9 m

Now , the volume of cube is given by

$\large \boxed{ \sf{Volume = {(side)}^{3} }}$

Thus ,

Volume = (9)³

Volume = 729 m³

$\sf \therefore{\underline{The \: volume \: of \: cube \: is \: 729 \: {m}^{3} }}$