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

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​

in progress 0
Iris 1 week 2021-09-14T06:29:11+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-14T06:30:33+00:00

    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

    ______________________

    0
    2021-09-14T06:30:57+00:00

    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} }}

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