Question

13. A certain quantity of wood costs Rs. 250 per m'. A solid cubical block pf such wood was
bought for Rs. 182.25. Calculate the volume of the block and use the method of factors to
find the length of one edge of the cube.
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Answer 1

Given,

A certain quantity of wood costs Rs. 250 per m³ . A solid cubical block of such wood was  bought for Rs. 182.25.

To find :

Calculate the volume of the block and use the method of factors to  find the length of one edge of the cube.

Solution :

Given , cost of wood = Rs. 250/m³

Cost of cubical block of wood = Rs. 182.25

Now,

⇒ Volume of block = Cost of cubical block of wood/Cost of wood

⇒ Volume of block = 182.25/250

⇒ Volume of block = 0.729 m³

∴ Volume of cubical block = 0.729 m³

Now we know that,

⇒ Volume of cube = a³

⇒ 0.729 = a³

⇒ a = ∛0.729

⇒ a = 0.9 m

⇒ a = (0.9 * 100) cm

⇒ a = 90 cm

∴ Length of each edge of cube = 0.9 m or 90 cm.

Answer 2

Cost of wood per m² = ₹ 250 /m³

Cost of wood bought = ₹ 182.25

To find the volume = 182.25/250

Volume of the block = 0.729 m³

Volume of block = (Edge of cube)³

→ ³√0.729 = Edge of cube

→ Edge of cube = 0.9 m