How many planks of size 2 m ×35 cm × 8 cm can be made from a wooden block 8 m long, 70 cm wide and 40 cm thick ?

The correct answer is Option 40.

To find the total number of wooden planks that can be made from the large wooden block, we need to divide the volume of the wooden block by the volume of a single plank.

First, let's ensure all dimensions are in the same unit of measurement (centimeters).

For the large wooden block:
Length ($L_1$) = 8 m = 800 cm
Width ($W_1$) = 70 cm
Thickness ($H_1$) = 40 cm

The volume of the wooden block is given by the formula:
$\text{Volume of block}=L_1\times W_1\times H_1$

$\text{Volume of block}=800\times 70\times 40=\mathrm{2,240,000}{\text{cm}}^3$

For a single wooden plank:
Length ($L_2$) = 2 m = 200 cm
Width ($W_2$) = 35 cm
Thickness ($H_2$) = 8 cm

The volume of one plank is given by:
$\text{Volume of plank}=L_2\times W_2\times H_2$

$\text{Volume of plank}=200\times 35\times 8=\mathrm{56,000}{\text{cm}}^3$

Now, calculate the number of planks:
$\text{Number of planks}=\frac{\text{Volume of block}}{\text{Volume of plank}}$

$\text{Number of planks}=\frac{\mathrm{2,240,000}}{\mathrm{56,000}}=40$

Hence, 40 planks can be made from the wooden block.