Answer

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Hint: Volume is measured in "cubic" units. The volume of a figure is the number of cubes required to fill it completely, like blocks in a box. Volume of a cube = side times side times side. Since each side of a square is the same, it can simply be the length of one side cube.

Complete step-by-step answer:

Volume of the tank is given to us and we know that the volume of the cubical tank will be cube of a length which in this case is unknown.

Therefore, let us consider a variable whose cube is $125000{m^3}$

Therefore,

${a^3} = 125000{m^3}$

To find the value of the length we have to solve the above equation,

Therefore,

$a = {125000^{\frac{1}{3}}}$

We can write the value of $125000$ as multiples of cubes.

Therefore,

$a = {\left( {125 \times 1000} \right)^{\frac{1}{3}}}$

$a = {\left( {{5^3} \times {{10}^3}} \right)^{\frac{1}{3}}}$

If we open the brackets, using the formula ${\left( {{a^m} \times {b^m}} \right)^{\frac{1}{m}}} = \left( {a \times b} \right)$

Therefore, on using the above formula, it becomes,

$a = 5 \times 10$

$a = 50$

Note: Make sure that you write the units.

Therefore, the lengths of the sides of the cubical tank are 50m each.

Complete step-by-step answer:

Volume of the tank is given to us and we know that the volume of the cubical tank will be cube of a length which in this case is unknown.

Therefore, let us consider a variable whose cube is $125000{m^3}$

Therefore,

${a^3} = 125000{m^3}$

To find the value of the length we have to solve the above equation,

Therefore,

$a = {125000^{\frac{1}{3}}}$

We can write the value of $125000$ as multiples of cubes.

Therefore,

$a = {\left( {125 \times 1000} \right)^{\frac{1}{3}}}$

$a = {\left( {{5^3} \times {{10}^3}} \right)^{\frac{1}{3}}}$

If we open the brackets, using the formula ${\left( {{a^m} \times {b^m}} \right)^{\frac{1}{m}}} = \left( {a \times b} \right)$

Therefore, on using the above formula, it becomes,

$a = 5 \times 10$

$a = 50$

Note: Make sure that you write the units.

Therefore, the lengths of the sides of the cubical tank are 50m each.

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