Why isn't the answer to TMUA-P1X-MGEO-07 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1X-MGEO-07 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1X-MGEO-07?

No — calculators are banned in the TMUA. TMUA-P1X-MGEO-07 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1X-MGEO-07?

TMUA-P1X-MGEO-07 is Paper P1 · Geometry (specification code M-Geo), level 3. Drill more of the same topic from this page.

TMUA-P1X-MGEO-07 — Paper P1 · Geometry · Level 3

P1M-GeoLevel 3~240s target

Spec: M-Geo · No calculator · ~240s

Two cylinders are mathematically similar with heights

4

cm and

6

cm. The smaller has total surface area

32\pi

^2

. What is the total surface area of the larger?

Options

$48\pi$ cm $^2$
$72\pi$ cm $^2$
$96\pi$ cm $^2$
$32\pi$ cm $^2$
$144\pi$ cm $^2$

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: similarity-powers, surface-volume-confusion. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Linear scale

= \frac{6}{4} = \frac{3}{2}

, so areas scale by

\frac{9}{4}

32\pi \times \frac{9}{4} = 72\pi

^2

. Trap:

48\pi

multiplies by

\frac{3}{2}

once — plausible if you apply the linear scale directly to an area.

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: surface-volume-confusion
P1M-GeoLevel 2
TMUA-P1-MGEO-007
A cylinder has radius 3 cm and height 10 cm. What is its volume in cm ^3?
Geometry
Open TMUA-P1-MGEO-007 →
More in this topic
P1M-GeoLevel 3
TMUA-P1-MGEO-015
Let a = (2, 5) and b = (-1, 3). What is |2a - b|?
Geometry
Open TMUA-P1-MGEO-015 →

Browse more

Loading…

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: surface-volume-confusion

P1M-GeoLevel 2

TMUA-P1-MGEO-007

A cylinder has radius 3 cm and height 10 cm. What is its volume in cm ^3?

Geometry

Open TMUA-P1-MGEO-007 →

TMUA-P1X-MGEO-07 — Paper P1 · Geometry · Level 3

Options

Keep practising

Master Geometry

TMUA-P1X-MGEO-07 — Paper P1 · Geometry · Level 3

Options

Keep practising

Master Geometry