Volume of solids

How to calculate the volume of solids, such as the cube, the sphere, the cylinder, the pyramid, the cone, the ellipsoid, and the rectangular prism is what you will learn here. 

As a warm up, take a look at the figure below looking like a pencil. How would you calculate the volume of the pencil above?

What important observation you need to make before calculating the volume of the pencil above? First, suppose that the pencil is made up of three different solids: a hemisphere, a cone, and a cylinder.

Therefore, volume of pencil = volume of cone + volume of cylinder + volume of hemisphere.

a. Volume of a cone  = (π×r²×h) / 3

π = 3.14, r  = 1.5 cm, and h = 3 cm

Volume of a cone  = (3.14×1.5²×3) / 3

Volume of a cone  = (3.14×2.25×3) / 3

Volume of a cone  = (21.195) / 3

Volume of a cone  = 7.065 cm³

b. Volume of a cylinder = π×r²×h

π = 3.14, r  = 1.5 cm, and h = 6 cm

Volume of a cylinder  = 3.14×1.5²×6 

Volume of a cylinder  = 3.14×2.25×6

Volume of a cylinder  = 42.39 cm³

c. Volume of a sphere = (2×π×r³) / 3

π = 3.14 and r  = 1.5 cm

Volume of a sphere = (2×3.14×1.5³) / 3

Volume of a sphere = (6.28×1.5³) / 3

Volume of a sphere = (6.28×3.375) / 3

Volume of a sphere = (21.195) / 3

Volume of a sphere = (21.195) / 3

Volume of a sphere = 7.065 cm³

volume of pencil = 7.065 cm³ + 42.39 cm³ + 7.065 cm³ = 56.52 cm³