Question

A log of wood of dimension 2 m x 20 cm x 10 cm is cut into small blocks of 10 cm x 5 cm x 4 cm.
How
many blocks will we get? What will be the total surface area of all these blocks?​

Answer 1

ANSWER

200 , 220cm²

Step-by-step explanation:

No. of blocks we get

= Vol. of big cuboid / Vol. of small cuboid

( 1m= 100cm )

So, 200×20×10/10×5×4 = 200 blocks

TSA of cuboid = 2(lb+bh+hl)

TSA of small blocks

2(10×5+5×4+4×10) = 2(50+20+40)

= 110×2 = 220cm²

Answer 2

Given:

• Dimensions of the log of wood = 2m × 20cm × 10cm
• Dimensions of one small block of wood = 10cm × 5cm × 4cm

To find:

• Number of blocks of wood that can be cut from the log of wood.
• Total surface area of all the blocks.

Solution:

Dimensions of the log of wood = 200cm × 20cm × 10cm [2m = 200cm]

$\boxed {\mathfrak {\pink {Volume\ of\ cuboid = l \times b \times h}}}$

Volume of log of wood = 200×20×10

Volume of log of wood = 40,000 cm³

$\:$

Dimensions of the block of wood = 10cm × 5cm × 4cm

Volume of block of wood = 10×5×4

Volume of block of wood = 200 cm³

$\:$

Now,

Total number of blocks of wood that can be cut from the log of wood = $\sf \dfrac {Volume\ of\ log\ of\ wood}{Volume\ of\ block\ of\ wood}$

$= \sf \dfrac {\cancel{40,000}\ \cancel{cm^{3}}}{\cancel{200}\ \cancel{cm^{3}}}$

= 200 blocks

$\:$

Now,

$\boxed {\mathfrak {\purple {T.S.A_{(cuboid)} = 2(lb+bh+hl)}}}$

T.S.A of 1 block of wood = 2 (10×5 + 5×4 + 4×10)

= 2 (50+20+40)

= 2×110

= 220 cm²

T.S.A of 200 blocks of wood = 220×200

T.S.A of 200 blocks of wood = 44,000 cm²

$\:$

Final answers:

• 200 blocks of dimensions 10cm × 5cm × 4cm can be cut from the log of wood of dimensions 2m × 20cm × 10cm.
• Total surface area of 200 blocks of wood is 44,000 cm².