Mensuration 3D (Volume & Surface Area)

Cuboid:

• Volume: $L \times B \times H$
• Total Surface Area (TSA): $2(LB + BH + HL)$
• Lateral Surface Area (LSA): $2(L+B) \times H$
• Diagonal: $\sqrt{L^2 + B^2 + H^2}$

• Volume: $a^3$
• TSA: $6a^2$
• LSA: $4a^2$
• Diagonal: $a\sqrt{3}$

Solid Cylinder:

• Volume: $\pi r^2 h$
• Curved Surface Area (CSA): $2\pi rh$
• Total Surface Area (TSA): $2\pi r(h+r)$

• Volume: $\pi h(R^2 - r^2)$
• TSA: $2\pi(R+r)(h+R-r)$

Cone:

• Slant Height ($l$): $\sqrt{h^2 + r^2}$
• Volume: $\frac{1}{3} \pi r^2 h$
• Curved Surface Area (CSA): $\pi rl$
• Total Surface Area (TSA): $\pi r(l+r)$

Sphere:

• Volume: $\frac{4}{3} \pi r^3$
• Surface Area: $4\pi r^2$

• Volume: $\frac{2}{3} \pi r^3$
• Curved Surface Area (CSA): $2\pi r^2$
• Total Surface Area (TSA): $3\pi r^2$

Volume: $\frac{1}{3} \pi h (R^2 + r^2 + Rr)$
CSA: $\pi l (R+r)$ where $l = \sqrt{h^2 + (R-r)^2}$
TSA: $\pi l (R+r) + \pi R^2 + \pi r^2$