Two equal disks inside a 7 cm by 4 cm rectangle touch its top and bottom sides. Their overlap has area 3 cm². Find the shaded area outside both disks.

01 / Standard#Your turn

Official paper · jm01-2021 · I.6 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The rectangle height is a circle diameter.

Hint 2

Subtract the union of the two disks, counting the overlap once.

Worked solution

Each radius is 2 cm, so each disk area is 4π.
$r=4/2=2,\quad|D_1|=|D_2|=4\pi$
Use inclusion–exclusion before subtracting from the rectangle.
$|D_1\cup D_2|=8\pi-3;\quad S=28-(8\pi-3)=31-8\pi$

A: 31−8π cm².

Checks and common pitfalls: The disks overlap; no external tangency between the disks is assumed.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Each radius is 2 cm, so each disk area is 4π.
$r=4/2=2,\quad|D_1|=|D_2|=4\pi$
Use inclusion–exclusion before subtracting from the rectangle.
$|D_1\cup D_2|=8\pi-3;\quad S=28-(8\pi-3)=31-8\pi$

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

2021 JM01