FINDING THE VOLUME OF 3D SHAPES

Volume of Prism, Cylinder, Cone or Sphere

	Area of square base x height Area of square = a2 Volume of cube = a3
	Area of rectangle x height Area of rectangle = l x w Volume = lwh
	= Area of triangle x height
	= Area of pentagon x height Area of pentagon = (3√3/2)a2 Volume = (3√3/2)a2 h
	= Area of circular base x height Area of circle = πr2 Volume = πr2h
	Volume = (1/3) base area x height
	Volume = (1/3) base area x height = (1/3)πr2h
	Volume = (4/3)πr3
	Volume = (2/3)πr3

Find the volume of the solid. If necessary, round your answer to the nearest whole number.

Problem 1 :

Solution :

By observing the figure, it is a rectangular prism.

Volume of the rectangular prism = length × Width × Height

We have,

Length = 9 in, Width = 4 in, and Height = 4 in

Volume = 9 × 4 × 4

= 144 in³

Problem 2 :

Solution :

By observing the figure, it is a triangular prism.

Volume of the triangular prism = Base area × Height

Length = 7 ft, Base = 6 ft, and Height = 10 ft

= 1/2 × 6 × 10 × 7

= 210  ft³

So, Volume of the triangular prisms is 210 ft³.

Problem 3 :

Solution :

By observing the figure, it is a cylinder.

Volume of the cylinder = πr²h

Given, Diameter (d) = 10 m, 

Radius (r) = d/2 = 10/2

Radius (r) = 5 m

Height of the cylinder = 7m.

Volume = (22/7) (5)² (7)

= 22 × 25

= 550 m³

So, volume of the cylinder is 550 m³.

Problem 4 :

Solution :

By observing the figure, it is a rectangular pyramid.

Volume of the rectangular pyramid = 1/3 × base area × Height

Length = 10 ft, Width = 10 ft, and Height = 12 ft

Volume = 1/3 × 10 × 10 × 12

V = 400 ft³

So, Volume of the pyramid is 400 ft³.

Problem 5 :

Solution :

By observing the figure, it is a Sphere.

Volume of the sphere = 4/3 πr³

Given, diameter (d) = 16 m

Radius (r) = d/2 = 16/2

r = 8 m

Volume = (4/3) (22/7) (8)³

= (4/3) (22/7) (512)

V = 2145 m³

So, volume of the sphere is 2145 m³.

Problem 6 :

Solution :

By observing the figure, it is a cone.

Volume of the cone = 1/3 πr²h

Radius (r) = 3 in, Height (h) = 5 in

Volume of the cone = (1/3) (22/7) (3)² (5)

= 330/7

V = 47 in³

So, Volume of the cone is 47 in³.