Reach for the Star | GCSE Mathematics

L070: Area and volume scale factors

Objective

Connect linear scale factors with area and volume change at the appropriate tier.

Calculator: Calculator allowed where labelled; non-calculator reasoning remains required.

Visual model for Area and volume scale factors
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for area and volume scale factors.

Core practice

Two similar solids have lengths ratio 3:4 and smaller surface area 54 cm². Find larger area.

Reasoning

Volume ratio of similar solids is 27:64. Find length and area ratios.

Exam-style

Solve an exam-style problem involving area and volume scale factors. Show working, include a check and interpret your answer.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L070: Area and volume scale factors

Objective: Connect linear scale factors with area and volume change at the appropriate tier.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: Two similar solids have lengths ratio 3:4 and smaller surface area 54 cm². Find larger area.

Deep challenge: Volume ratio of similar solids is 27:64. Find length and area ratios.