Question

A cylindrical hole of diameter 30 cm is bored through a cuboid wooden block with side 1 meter as shown in fig 6.47. Find the volume of the object so formed ($\mathrm{\pi }=3.14$)

Answer 1

DISCLAIMER: Instead of cuboid, it should be cubical in the question.

Given:
Diameter of the cylindrical hole = 30 cm
Side of the cubical wooden block = 1 m = 100 cm
Height of the cylindrical hole = 100 cm
∴ Radius of the cylindrical hole = $\frac{30}{2}$ = 15 cm
Now,
Volume of the cylindrical hole = $\mathrm{\pi }$r²h
= 3.14 × (15)² × 100
= 70650 cm³
And,
Volume of the cubical wooden block = (Side)³
= (100)³
= 1000000 cm³
Thus, we have:
Volume of the block so formed = Volume of the cubical wooden block $-$ Volume of the cylindrical hole
= 1000000 $-$ 70650
= 929350 cm³