Question

How many planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, and assuming that there is no wastage?

Answer 1

Hint: Here, first calculate the volume of one plank using the formula of cuboid, then find the volume of the wooden block. As in conversion of shapes, volume remains the same. So, divide the volume of the wooden block by the volume of one plank to get the number of planks.

Complete step by step answer:
Given, dimensions of smaller plank is 2 m × 25 cm × 8 cm or 200 cm× 25 cm × 8 cm
Volume of smaller plank, V1 = 200 cm× 25 cm × 8 cm = 40000 cm3
[Volume of a cuboid = Length × Breadth × Height]
Also given, dimensions of a wooden block is 5 m × 70 cm × 32 cm or 500 cm× 70 cm ×32 cm
Volume of smaller plank, V2 = 500 cm× 70 cm × 32 cm = 1120000 cm3
Let ‘n’ be the number of planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick.
n × volume of plank = volume of wooden block
n × V1 = V2
n = $\dfrac{{{V_2}}}{{{V_1}}}$
⇒ n = $\dfrac{{1120000}}{{40000}} = \dfrac{{112}}{4} = 28$
Therefore, number planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, and assuming that there is no wastage is 28.

Note:
In these types of questions, always remember that in conversion of solid from one shape to another shape, volumes of the two remain the same. Equate the volumes of the two to get the final answer.