Formulas for volume and surface area of 3D shapes

📦 1. Prisms (e.g. cuboid)

7

🔹 Volume

Volume=base area×height\text{Volume} = \text{base area} \times \text{height}Volume=base area×height

For a cuboid:

V=l×w×hV = l \times w \times hV=l×w×h

🔹 Surface Area

Add all the faces:

For cuboid:

SA=2(lw+lh+wh)SA = 2(lw + lh + wh)SA=2(lw+lh+wh)

🔺 2. Pyramid

6

🔹 Volume

V=13×base area×heightV = \frac{1}{3} \times \text{base area} \times \text{height}V=31​×base area×height

🔹 Surface Area

SA=base area+triangular facesSA = \text{base area} + \text{triangular faces}SA=base area+triangular faces

(You usually need slant height)

🥫 3. Cylinder

5

🔹 Volume

V=πr2hV = \pi r^2 hV=πr2h

🔹 Surface Area

SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi rhSA=2πr2+2πrh

(top + bottom + curved surface)

🍦 4. Cone

5

🔹 Volume

V=13πr2hV = \frac{1}{3}\pi r^2 hV=31​πr2h

🔹 Surface Area

SA=πr2+πrlSA = \pi r^2 + \pi rlSA=πr2+πrl

(where l = slant height)

⚡ THE IMPORTANT PART (Science link)

📊 Surface Area to Volume Ratio (SA:V)

👉 This is what your science test really cares about

SA:V=surface areavolume\text{SA:V} = \frac{\text{surface area}}{\text{volume}}SA:V=volumesurface area​