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Mathematics

A certain quantity of wood costs ₹250 per m3. A solid cubical block of such wood is bought for ₹182.25. Calculate the volume of the block and use the method of factors to find the length of one edge of the block.

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Answer

Given,

Cost of 1 m3 wood = ₹250

By unitary method,

For ₹250, quantity of wood = 1 m3

For ₹182.25, quantity of wood = 182.25×1250\dfrac{182.25 \times 1}{250}

= 1822525000\dfrac{18225}{25000}

= 7291000\dfrac{729}{1000}

= 0.729 m3.

By formula,

Volume of cuboidal block = (side)3

∴ (side)3 = 0.729 m3

⇒ (side)3 = 7291000\dfrac{729}{1000}

⇒ side = 72910003\sqrt[3]{\dfrac{729}{1000}}

On factorising 729 and 1000 we get,

⇒ side = 3×3×3×3×3×32×2×2×5×5×53\sqrt[3]{\dfrac{3 \times 3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 5 \times 5 \times 5}}

⇒ side = 3×32×5=910\dfrac{3 \times 3}{2 \times 5} = \dfrac{9}{10} = 0.9 m.

Hence, volume of block = 0.729 m3 and the length of one edge of the block is 0.9 m.

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