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 =$\Pi&space;r^{2}h$

Curved surface area =$2\Pi&space;rh$

Total surface area =  $2\Pi&space;r(h+r)$

• CONE:

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

Volume = $\frac{1}{3}\Pi&space;r^{2}$

Curved surface area = $\Pi&space;rl$

Total surface area = $\Pi&space;r(l+r)$

• SPHERE:

Example is ball

Volume = $\frac{4}{3}\Pi&space;r^{3}$

Curved surface area = $4\Pi&space;r^{2}$

Total surface area = $4\Pi&space;r^{2}$

• HEMISPHERE:

Volume = $2\Pi&space;r^{3}$

Curved surface area = $2\Pi&space;r^{2}$

Total surface area = $3\Pi&space;r^{2}$

• FRUSTUM:

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

Curved surface area = $\Pi&space;(R+r)l$

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

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

• 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 = $3\times&space;\frac{\sqrt{3}}{4}a^{2}$

Total surface area = $4\times&space;\frac{\sqrt{3}}{4}a^{2}=\sqrt{3}a^{2}$