Why isn't the answer to TMUA-P1-MGEO-016 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MGEO-016 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MGEO-016?

No — calculators are banned in the TMUA. TMUA-P1-MGEO-016 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MGEO-016?

TMUA-P1-MGEO-016 is Paper P1 · Geometry (specification code M-Geo), level 3. Drill more of the same topic from this page.

TMUA-P1-MGEO-016 — Paper P1 · Geometry · Level 3

P1M-GeoLevel 3~210s target

Spec: M-Geo · No calculator · ~210s

Two cones are mathematically similar with heights

3

cm and

9

cm. The smaller cone has volume

20

^3

. What is the volume of the larger cone?

Options

$60$ cm $^3$
$180$ cm $^3$
$1620$ cm $^3$
$27$ cm $^3$
$540$ cm $^3$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: mgeo-similarity, similarity-powers, area-volume-confusion. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Linear scale

= \frac{9}{3} = 3

, so volumes scale by

3^3 = 27

20 \times 27 = 540

^3

.
Trap:

180

^3

multiplies by

3^2 = 9

— the square law is for areas, not volumes.

Keep practising

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Keep practising

Same topic · same level

P1M-GeoLevel 3

TMUA-P1-MGEO-009

A right circular cone has base radius 5 cm and slant height 13 cm. What is its volume in cm ^3?

Geometry

Open TMUA-P1-MGEO-009 →

Same trap: mgeo-similarity

P1M-GeoLevel 2

TMUA-P1-MGEO-013

Two triangles are mathematically similar. Two corresponding sides are 4 cm and 10 cm. The smaller triangle has area 24 c…

Geometry

Open TMUA-P1-MGEO-013 →

TMUA-P1-MGEO-016 — Paper P1 · Geometry · Level 3

Options

Keep practising

Master Geometry

TMUA-P1-MGEO-016 — Paper P1 · Geometry · Level 3

Options

Keep practising

Master Geometry