What is covered in Grade 11 Mathematics Measurement?

Surface area and volume of combinations of 3D objects. Effect of scaling dimensions on surface area and volume.

Is Grade 11 Measurement tested in Paper 1 or Paper 2?

Grade 11 Mathematics Measurement is assessed in Paper 2 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Measurement taught in Grade 11 Mathematics?

Measurement is taught in Term 4 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Measurement on the CAPS curriculum?

Yes. Measurement is part of the official CAPS Mathematics curriculum for Grade 11, Term 4 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 11 Mathematics

Grade 11 · Term 4Mathematics

Measurement

We apply surface area and volume formulas to more complex composite solids and investigate the effect of scaling on surface area and volume.

Week 5

11.1 Composite Solids & Scale Factors

Calculate surface area and volume of complex composite solids
Investigate the effect of multiplying dimensions by a constant factor $k$
Apply to real-world contexts

🌍

Real-World Connection

Engineers designing larger versions of equipment must know that doubling all dimensions makes volume 8 times larger but surface area only 4 times larger. This is why large animals need different body structures than small ones — volume (weight) grows faster than surface area (for heat loss).

Property / Rule

Scale Factor Effect on Area & Volume

If all linear dimensions are multiplied by $k$ : Surface area multiplies by $k^2$ ; Volume multiplies by $k^3$ .

\text{SA}_{\text{new}}=k^2\cdot\text{SA}_{\text{original}};\quad V_{\text{new}}=k^3\cdot V_{\text{original}}

🌍 Real-World Context

The Square-Cube Law: cells must be small because their surface area (for nutrient/waste exchange) grows as $r^2$ while their volume (metabolic demand) grows as $r^3$ . A cell that doubles in size has 4× the exchange surface but 8× the demand — it cannot sustain itself.

Worked Examples

Worked Example

Scale factor on a cylinder

Problem

r=3

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge1 mark

If all dimensions are doubled, by what factor does the volume change?

L1 · Knowledge2 marks

A cube has side 4 cm. Find its volume.

L2 · Routine Procedures4 marks

A sphere has surface area

100\pi

. Find its radius and volume.

L2 · Routine Procedures4 marks

A cone has

r=6

h=8

. Find the slant height and total surface area.

L3 · Complex Procedures4 marks

Two similar cylinders have volumes

64\text{ cm}^3

and

216\text{ cm}^3

. Find the ratio of their radii.

L3 · Complex Procedures4 marks

A solid consists of a hemisphere (r=6) sitting on top of a cylinder (r=6, h=10). Find the total volume.

L4 · Problem Solving5 marks

A frustum (truncated cone) has top radius 3, bottom radius 6 and height 8. Find its volume.

L4 · Problem Solving4 marks

A solid metal ball of radius 9 cm is melted and recast into small balls each of radius 1.5 cm. How many small balls are made?

Probability