A sector of a circle of radius 4 has angle 3π/4 radians. What is its area?

Worked solution for TMUA-P1-MM4-008 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM4-008 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-008 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM4-008?

No — calculators are banned in the TMUA. TMUA-P1-MM4-008 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM4-008?

TMUA-P1-MM4-008 is Paper P1 · Trigonometry (specification code MM4), level 2. Drill more of the same topic from this page.

TMUA-P1-MM4-008 — Paper P1 · Trigonometry · Level 2

P1MM4Level 2~180s target

Spec: MM4 · No calculator · ~180s

A sector of a circle of radius

4

has angle

\frac{3\pi}{4}

radians. What is its area?

Options

$3\pi$
$12\pi$
$8\pi$
$6\pi$
$\dfrac{3\pi}{2}$

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: sector-area, missing-half. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Sector area

= \frac{1}{2}r^2\theta = \frac{1}{2}(16)\left(\frac{3\pi}{4}\right) = 6\pi

. Trap:

3\pi

forgets the

\frac{1}{2}

— plausible since the arc-length formula has no half.

Keep practising

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Step up a level
P1MM4Level 3
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Browse more

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Keep practising

Same topic · same level

P1MM4Level 2

TMUA-P1-MM4-005

A triangle has sides of length 5 and 7 with included angle 60^°. What is the length of the third side?

Trigonometry

Open TMUA-P1-MM4-005 →

Same trap: sector-area

P1M-GeoLevel 2

TMUA-P1-MGEO-008

A sector of a circle of radius 8 cm has angle 90^°. What is its area in cm ^2?

Geometry

Open TMUA-P1-MGEO-008 →

Step up a level

P1MM4Level 3

TMUA-P1-MM4-011

A triangle has sides of length 4, 5 and 6. What is the cosine of its largest angle?

Trigonometry

Open TMUA-P1-MM4-011 →

TMUA-P1-MM4-008 — Paper P1 · Trigonometry · Level 2

Options

Keep practising

Master Trigonometry

TMUA-P1-MM4-008 — Paper P1 · Trigonometry · Level 2

Options

Keep practising

Master Trigonometry