Question

Q: From a cylindrical wooden log of length 30 cm and base radius 7√2 cm, maximum cuboid of square base is made. Find the volume of wood wasted.

Answer 1

Find the volume of the cylindrical log:

Volume = πr²h

Volume = π(7√2)²(30) = 9240 cm³

Find the max length for the square:

*See attachment:

a² + b² = c²

(7√2)² + (7√2)² = c²

98 + 98 = c²

c² = 196

c = √196

c = 14 cm

Find the volume of the cuboid:

Volume = Length x Breadth x Height

Volume = 14 x 14 x 30 = 5880 cm³

Find the volume of the wood wasted:

Volume wasted = 9240 - 5880 = 3360 cm³

Answer: The volume of the wood wasted is 3360 cm³

Answer 2

Solutions :-


We have,

Length = 30 cm
Radius = 7√2 cm


Find the volume of cylindrical wooden log :-

Volume of cylinder = πr²h cubic unit
= 22/7 × (7√2)² × 30 cm³
= 9240 cm³


Find the maximum length of the side of square :-

By Pythagoras theorem,

p² + b² = h²
=> (7√2)² + (7√2)² = h²
=> 98 + 98 = h²
=> h² = 196
=> h = √196 = 14



Find the volume of cuboid :-

Volume of cuboid = l × b × h cubic unit
= 14 × 14 × 30 cm³
= 5880 cm³




Now,

Find the volume of wood wasted :-

Volume of wasted wood = volume of cylindrical wooden log - volume of cuboid

= (9240 - 5880) cm³
= 3360 cm³



Answer : The volume of wood wasted = 3360 cm³