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Grade 5 (age 10-11)

grade 5 Rectangular Solid: Surface Area & Volume

Rectangular Solid: Surface Area & Volume

A rectangular solid is a box wrapped in six rectangles, with 6 faces, 12 edges, and 8 vertices, and opposite faces match. Unfold it flat and it becomes a net; the six face areas add to the surface area, and width times depth times height is the volume. Change the width, depth, and height and the 3D box and its net change with them.

What is a Rectangular Solid?

📦 A 3D shape like a box
①Surrounded by 6 rectangles
②Opposite faces are identical in shape and size
③8 vertices, 12 edges, 6 faces!
4
2
3

Understanding via Net

📋 Unfold the box → 6 rectangles
①Cut the box and lay it flat → net
②Same-color faces face each other (same shape and size)
③Sum all face areas = surface area!

Summary

Surface Area
SA = 2 × (W×H + H×D + W×D)
Sum of three pairs of rectangles
Volume
V = W × D × H
Base area × height
Current Box
SA=52cm², Vol=24cm³
width × depth × height = 4×2×3 rectangular solid
🎯 Key Points
①Rectangular solid: 3D shape made of 6 rectangles
②Surface area: sum of all 6 faces
③Volume: width × depth × height
④A cube is a special case with equal edges
⑤Units: area in cm², volume in cm³

Examples and Unit Test

Example 1
Find the volume of a rectangular solid with width 3 cm, depth 2 cm, height 4 cm.
1
Volume of a rectangular solid = width × depth × height.
2
3 × 2 × 4 = 24, so the volume is 24 cm³.
▸ 24 cm³
The unit of volume is cm³ (cubic centimeter).
Example 2
Find the surface area of a rectangular solid with width 3 cm, depth 2 cm, height 4 cm.
1
Surface area = 2 × (width×depth + depth×height + width×height).
2
2 × (3×2 + 2×4 + 3×4) = 2 × (6 + 8 + 12) = 2 × 26 = 52 cm².
▸ 52 cm²
Surface area is the sum of all 6 faces (3 pairs), in cm².
Unit Test
What is the volume of a cube with edge 2 cm?
①6 cm³
②8 cm³
③4 cm³
④12 cm³
▸ ② 8 cm³
1
A cube is a rectangular solid with equal width, depth, and height.
2
Volume = 2 × 2 × 2 = 8 cm³.
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