Dimension Drafts Reference Sheet
STUDENT REFERENCE CARD
DIMENSION DRAFTS
A Step-by-Step Guide to 3D Surface Area & Volume
NAME
DATE
Color Guide:
r = radius h = vertical height l = slant height B = base area | L = length P = perimeter
1. Prisms (Rectangular & Triangular)
Polyhedrons
A. Rectangular Prism 6 rectangular faces
l (length) w h
Volume V = l • w • h
Surface Area SA = 2(lw + lh + wh)
📐 Example: l = 6 cm, w = 4 cm, h = 5 cm
Volume Step:
V = 6 • 4 • 5 = 120 cm3
Surface Area Step:
SA = 2(6•4 + 6•5 + 4•5)
SA = 2(24 + 30 + 20) = 2(74) = 148 cm2
B. Triangular Prism 2 bases, 3 rectangles
L h b
Volume V = B • L B = 1/2 • b • h
Surface Area SA = 2B + P•L P = b + s1 + s2
📐 Example: b = 6, h = 4, L = 10, s1 = 5, s2 = 5
Volume Step: B = 1/2 • 6 • 4 = 12 cm2
V = 12 • 10 = 120 cm3
Surface Area Step: P = 6 + 5 + 5 = 16 cm
SA = 2(12) + (16)(10) = 184 cm2
2. Cylinders
Curved Solids
h r
Volume V = π • r2 • h
Surface Area SA = 2πr2 + 2πrh
📐 Worked Example (π ≈ 3.14)
Find metrics for a cylinder with radius r = 3 in and height h = 8 in.
1
Solve Volume:
V = π • r2 • h ≈ 3.14 • 32 • 8
V ≈ 3.14 • 9 • 8 = 226.08 in3
2
Solve Surface Area:
SA = 2πr2 + 2πrh ≈ 2(3.14)(32) + 2(3.14)(3)(8)
SA ≈ 56.52 + 150.72 = 207.24 in2
DIMENSION DRAFTS: PAGE 1 OF 2 FORMULAS & WORKED EXAMPLES
DIMENSION DRAFTS Reference Sheet Part 2: Curved Solids & Pyramids
3. Cones
Curved
h r l
V = 1/3 • πr2h
SA = πr2 + πrl
📐 Example: r = 5 cm, h = 12 cm
1. Find Slant Height (l):
l = √(52 + 122) = 13 cm
2. Volume Step:
V = 1/3(3.14)(52)(12) = 314 cm3
3. Surface Area Step:
SA = 3.14(25) + 3.14(5)(13) = 282.6 cm2
4. Square Pyramids
Polyhedron
h l s
V = 1/3 • s2 • h
SA = s2 + 2sl
📐 Example: s = 6 m, h = 4 m
1. Find Slant Height (l):
l = √(42 + (6/2)2) = 5 m
2. Volume Step:
V = 1/3(62)(4) = 48 m3
3. Surface Area Step:
SA = 62 + 2(6)(5) = 96 m2
5. Spheres
Perfect Round
r
V = 4/3 • πr3
SA = 4 • πr2
📐 Worked Example: r = 6 ft (π ≈ 3.14)
1. Volume Step:
V = 4/3(3.14)(63) = 1.33 • 3.14 • 216 ≈ 904.32 ft3
2. Surface Area Step:
SA = 4(3.14)(62) = 4 • 3.14 • 36 ≈ 452.16 ft2
Troubleshoot
1. Height vs. Slant:
In cones & pyramids, vertical height (h) is inside perpendicular. Slant (l) goes down the outer wall.
2. Metric Units:
Linear units are flat lines. Area cover is squared (2). Volume capacities are cubic (3).
3. Diameter Caution:
Always check if you are given diameter (d). If so, divide by 2 first to get radius (r = d/2).
DIMENSION DRAFTS: PAGE 2 OF 2 FORMULAS & WORKED EXAMPLES
