Mensuration 3D: Formula Sheet

Volume & Surface Area Reference

1. Box Shapes (Prisms)

Shape Lateral/Curved Area Total Surface Area Volume
Cuboid
(l, b, h)		 $$ 2h(l+b) $$ $$ 2(lb+bh+hl) $$ $$ l \times b \times h $$
Cube
(side ‘a’)		 $$ 4a^2 $$ $$ 6a^2 $$ $$ a^3 $$

2. Cylinders & Cones

Shape CSA (Curved Area) TSA (Total Area) Volume
Cylinder
(r, h)		 $$ 2\pi rh $$ $$ 2\pi r(r+h) $$ $$ \pi r^2 h $$
Cone
(r, h, l)		 $$ \pi rl $$ $$ \pi r(l+r) $$ $$ \frac{1}{3}\pi r^2 h $$

*Note: For Cone, Slant height $$ l = \sqrt{r^2 + h^2} $$

3. Spheres

Sphere

Surface Area: $$ 4\pi r^2 $$

Volume: $$ \frac{4}{3}\pi r^3 $$

Hemi-sphere

CSA: $$ 2\pi r^2 $$

TSA: $$ 3\pi r^2 $$

Volume: $$ \frac{2}{3}\pi r^3 $$

4. Advanced Shapes

Frustum of Cone
(R = big radius, r = small radius, l = slant, h = height)

  • Slant Height (l): $$ \sqrt{h^2 + (R-r)^2} $$
  • CSA: $$ \pi l(R+r) $$
  • TSA: $$ \pi l(R+r) + \pi(R^2 + r^2) $$
  • Volume: $$ \frac{1}{3}\pi h (R^2 + r^2 + Rr) $$
Hollow Cylinder
(R = Outer radius, r = Inner radius, h = height)

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

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