Mensuration Part 8

Important Formula:

  • CUBE:

Volume = a^{3}

Curved surface area = 4a^{2}

Total surface area = 6a^{2}

  • CUBOID:

Volume = l*b*h

Curved surface area = 2(l+b)*h

Total surface area = 2(lb+bh+hl)

diagno1 =\sqrt{l^{2}+b^{2}+h^{2}}

  • CYLINDER:

Volume =\Pi r^{2}h

Curved surface area =2\Pi rh

Total surface area =  2\Pi r(h+r)

  • CONE:

l=slant height = \sqrt{h^{2}+r^{2}}

Volume = \frac{1}{3}\Pi r^{2}

Curved surface area = \Pi rl

Total surface area = \Pi r(l+r)

  • SPHERE:

Example is ball

Volume = \frac{4}{3}\Pi r^{3}

Curved surface area = 4\Pi r^{2}

Total surface area = 4\Pi r^{2}

  • HEMISPHERE:

Volume = 2\Pi r^{3}

Curved surface area = 2\Pi r^{2}

Total surface area = 3\Pi r^{2}

  • FRUSTUM:

Volume = \frac{1}{3}\Pi (R^{2}+r^{2}+rR)h

Curved surface area = \Pi (R+r)l

Total surface area = \Pi (R^{2}+r^{2}+Rl+rl)

l=\sqrt{h^{2}+(R-r)^{2}}

  • PRISM:

         

Volume=Area of base * Height

Lateral surface area = Perimeter of base * height

Total surface area = L.S.A+2*Area of base

  • Tetrahedron:

Volume =\frac{\sqrt{2}}{12}a^{3}

Lateral surface area = 3\times \frac{\sqrt{3}}{4}a^{2}

Total surface area = 4\times \frac{\sqrt{3}}{4}a^{2}=\sqrt{3}a^{2}

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