A cylinder’s radius increases 30% while its height decreases 30%. Find the volume change.

01 / Standard#Your turn

Official paper · jm01-2025 · I.3 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Cylinder volume is proportional to radius squared times height.

Hint 2

Use multipliers 1.3 and 0.7.

Worked solution

Square only the radius multiplier.
$\frac{V_{\rm new}}{V_{\rm old}}=(1.3)^2(0.7)=1.183$
Subtract one to obtain the proportional increase.
$(1.183-1)\cdot100\%=18.3\%$

A: increase 18.3%.

Checks and common pitfalls: Equal percentage changes in radius and height do not cancel.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Square only the radius multiplier.
$\frac{V_{\rm new}}{V_{\rm old}}=(1.3)^2(0.7)=1.183$
Subtract one to obtain the proportional increase.
$(1.183-1)\cdot100\%=18.3\%$

Think first. Reveal a hint when the class is ready.

2025 JM01