Question

the trunk of a tree is a right circular cylinder 3.5 m in radius and 30 m high. Find the

volume of the timber which must be cut off just enough to reduce it to a rectangular

parallelopiped on a square base​

Answer 1

Given : trunk of a tree is a right circular cylinder 3.5 m in radius and 30 m high.

Tree is reduced  to a rectangular  parallelepiped on a square base​

To Find  : Minimum volume of the timber which must be cut off

Solution:

Volume of Tree =  πr²h

r = 3.5 m = 7/2  m

h = 30 m

π = 22/7

=  (22/7)(7/2)²(30)

=  1,155 m³

We need to find maximum size of Square base in circular base

which will be when  Diameter will be be Diagonal of Square

Diagonal of Square  = 7 m

Side of Square = 7/√2 m

Area of Square base = 49/2 m²

Volume of rectangular  parallelepiped = (49/2) 30

= 735 m³

Volume of the timber which must be cut = 1,155  - 735

= 420 m³

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Answer 2

Step-by-step explanation:

Given The trunk of a tree is a right circular cylinder 3.5 m in radius and 30 m high. Find the volume of the timber which must be cut off just enough to reduce it to a rectangular parallelopiped on a square base

• Now diameter d = 3.5 m + 3.5 m = 7 m
• Let the side of the square base be m
•               So m^2 + m^2 = (7m)^2
•                       2m^2 = 49 m^2
•                       m^2 = 49/2
•                       m = 7 / √2 m
• So volume v = 7/√2 x 7/√2 x 30 m^3
•                        = 49 x 15
•                         = 735 m^3 is the required volume.

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