Ms. Terkper's Digital Classroom

Unit 3 Review: Measurement

SI & Imperial units • Conversions • Surface area & volume of prisms, cylinders, pyramids, cones, spheres

SI & Imperial Unit Conversions Surface Area Volume Nets & Lateral Area

What You Should Be Able To Do

  • Identify and use appropriate SI and Imperial units for length, area, and volume.
  • Convert within SI, within Imperial, and between SI ↔ Imperial using given conversion factors.
  • Choose correct surface-area and volume formulas for prisms, cylinders, pyramids, cones, and spheres.
  • Solve multi-step problems including composite solids and real-world contexts.
  • Communicate with correct units, labels, and reasonable precision.
Progress autosaves to this device.

Video Library

SI vs. Imperial Units (Overview)

Common units, when to use each, and pitfalls.

youtube.com – “SI and Imperial units overview math”

Conversions & Dimensional Analysis

Converting within/between systems using the factor-label method.

youtube.com – “unit conversion ladder method dimensional analysis”

Prisms & Cylinders – SA & Volume

Nets, lateral area, total surface area, composite shapes.

youtube.com – “surface area and volume prisms cylinders”

Pyramids, Cones & Spheres – SA & Volume

Slant height vs. height, curved surface area, caps.

youtube.com – “surface area and volume cones pyramids spheres”

Tools

Quick Unit Converter

Notes: 1 in = 2.54 cm • 1 ft = 0.3048 m • 1 yd = 0.9144 m • 1 mi = 1.60934 km • 1 kg = 2.20462 lb • 1 L = 1000 mL • 1 US gal = 3.78541 L • 1 cm³ = 1 mL.

Formula Quick-Reference

SolidSurface AreaVolume
Right PrismSA = 2B + PhV = Bh
CylinderSA = 2\pi r^2 + 2\pi rhV = \pi r^2 h
PyramidSA = B + \tfrac12 P \ell (ℓ = slant)V = \tfrac13 Bh
ConeSA = \pi r^2 + \pi r \ell (ℓ = slant)V = \tfrac13 \pi r^2 h
SphereSA = 4\pi r^2V = \tfrac43 \pi r^3

Tip: For composite solids, split into parts, compute each SA/volume, then add/subtract as needed (subtract overlapped faces for SA!).

Unit 3 Quizzes

Quiz 1: Units & Conversions

SI vs. Imperial, within/between systems, dimensional analysis.

Quiz 2: Surface Area & Volume

Prisms, cylinders, pyramids, cones, spheres, composite solids.

Downloadable Review

Get the full set of Unit 3 practice questions as a printable PDF.

Download PDF

Quick Practice Scratchpad

Ideas: Convert 5.2 ft to cm; Find SA of a cylinder (r=4 cm, h=12 cm); Volume of a cone (r=3 m, h=10 m).