USING POLYNOMIAL TO FIND VOLUME OF 3D SHAPES

Find the volume of the 3D shapes given below.

Problem 1 :

Solution :

Length = 2x, width = x and height = 3x

Volume of cuboid = Base area ⋅ height

Base area = 2x (x) ==> 2x²

Volume of cuboid = 2x²(3x)

V = 6x³

Problem 2 :

Solution :

length = c, Breadth = a, Height = b

Base is in the shape of triangle. 

Area of triangle = 1/2 × base x height

= (1/2) ⋅ a ⋅ b

Volume of triangular prism = Base area × height

= 1/2 × a × b × c

V = (1/2)abc

Problem 3 :

Solution :

Height = 4r, Diameter = 2r, Radius r = 2r/2 = r

Base area = πr²

Volume of cylinder = Base area x height

= π × r² × 4r

V = 4πr³

Problem 4 :

Solution :

Hight = 3x, Diameter = 2x, Radius = 2x/2 = x

Volume of cone = 1/3 ×Base area x height

Base area = πr²

= πx²

= (1/3) × π x² × 3x

V = πx³

Problem 5 :

Solution :

Base = a, Height = h

Volume of pyramid = 1/3 × (base area) × height

Base is in the shape of square. Area of base square = a²

= 1/3 × a² × h

V = a²h/3

Problem 6 : 

Solution :

Height = 4x, Diameter = 2x, Radius = 2x/2 = x

Base is in the shape of semi circle.

Area of semi circle = (1/2)πr² ==> (1/2)πx²

Volume of semi circular = 1/2 × πr²h

= 1/2 × π × x² × 4x

V = 2πx³