5. A cylindrical groove is made in a cylindrical 21 cm long solid piece of wood. The groove
is filled with lead and this cylindrical lead block is of same length as that of the wooden
cylinder is 3 cm and the outer diameter of the wooden cylinder is 12 cm, find the volume of
the wood and that of the lead. (Take π= 22/7 )
Answers
GIVEN:
A groove is made in a cylindrical long solid piece of wood.
Length of the wood = Height = 21cm
Length of cylindrical block is of same length as that of wooden cylinder.
i.e Diameter of cylindrical lead block = 3cm
Radius of lead block = 3/2 = 1.5cm
Volume of lead = πr²h
= 22/7 × (1.5)² × 21
= 22 × (1.5)² × 3
= 148.50cm³
Let's find the volume of wooden cylinder
Outer diameter of wooden cylinder = 12cm
Radius of wooden cylinder = 12/2 = 6cm
Height of wooden cylinder = 21cm
Volume of wooden cylinder = πr²h
= 22/7 × 6² × 21
= 22 × 36 × 3
= 66 × 36
= 2376cm³
Now, to find the volume of wood, we should subtract volume of groove with lead from volume of wooden cylinder.
= 2376 - 148.5
= 2227.5 cm³
Therefore, the volume of wood is 2227. 50 cm³.
Answer:
148.50 is your answer mate