Question

the trunk of a tree is a right cylinder 1.5m radius and 10m high. what is the volume of the timber which remains when the trunk is trimmed just enough to reduce to a rectangular parallelogram on a square base​

Answer 1

Answer:

45 m^3

Step-by-step explanation:

Given The trunk of a tree is a right cylinder 1.5m radius and 10m high. what is the volume of the timber which remains when the trunk is trimmed just enough to reduce to a rectangular parallelogram on a square base​

We know that diameter of circular base = diagonal of square base

diagonal AC = BD

From triangle AOB,

   AB^2 = 1.5^2 + 1.5^2

  AB^2 = 2.25 + 2.25

 AB =  4.5 m^2

So area of square base of tree is given by 4.5 m^2

We know that

Volume = area of square base x height

 volume = 4.5 m^2 x 10 m

 volume = 45 m^3

Answer 2

Given : trunk of a tree is a right circular cylinder 1.5 m in radius and 10 m high.

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

To Find  : the volume of the timber which remains

Solution:

Radius of base = 1.5m

=> Diameter = 3 m

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  = 3  m  = Diameter of circular base

Side of Square = 3/√2 m

Area of Square base =  9/2 m²

Volume of rectangular  parallelepiped = ( 9/2) 10

= 45 m³

Volume of the timber which remains = 45 m³

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