Question

What will be the length of each edge of the greatest cube that can be obtainedby cutting a woolen cuboid of length 175cm breadth 105cm and height 63cm ?

Answer 1

Hi,

Answer: 105 cm
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➡️Solution:
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Volume of cuboid =
$length \: \times breadth \: \times height$

length= 175cm

breadth = 105cm

height = 63cm

Volume =
$175 \times 105 \times 63 \: {cm}^{3} \\ \\ = 1157625 \: {cm}^{3}$
The largest cube so formed from the given volume =

Since volume of cube = ${a}^{3}$

a = side of cube

${a}^{3} = 1157625 \\ \\ a = \sqrt[3]{1157625} \\ \\ a = \sqrt[3]{3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7} \\ \\ a = 3 \times 5 \times 7 \\ \\ a = 105 \: cm$

Thus largest cube so formed is of 105 cm each edge.

Hope it helps you.