A vertical cylindrical tank has radius 3 m, height 8 m and initial water depth 5 m. A radius-2 m sphere is fully submerged. Find the water rise.

01 / Standard#Your turn

Official paper · jm01-2023 · I.9 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The displaced water volume equals the sphere volume.

Hint 2

Divide by the tank’s horizontal cross-sectional area.

Worked solution

Find the displaced volume.
$V=\frac43\pi(2)^3=\frac{32\pi}3$
Convert volume to height and check no overflow.
$\Delta h=\frac{32\pi/3}{9\pi}=\frac{32}{27},\quad5+32/27<8$

E: 32/27 m.

Checks and common pitfalls: Use the tank area, not the sphere’s great-circle area.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Find the displaced volume.
$V=\frac43\pi(2)^3=\frac{32\pi}3$
Convert volume to height and check no overflow.
$\Delta h=\frac{32\pi/3}{9\pi}=\frac{32}{27},\quad5+32/27<8$

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

2023 JM01