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Problem 382

Geometry Difficulty 2.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2024

A block of wood in the shape of a rectangular prism has length
$4\text{ cm}$ , width $4\text{ cm}$ , and height $7\text{ cm}$ . A cylindrical hole with
radius $1\text{ cm}$ is drilled
through the centre, as shown.

To the nearest $\text{cm}^3$ , what
is the volume of the block of wood after the hole is drilled? (Note: The
volume of a cylinder with radius $r$
and height $h$ is $\pi r^2h$ .)

Pick one

Official solution

Before the hole was drilled, the volume of the block of wood was
$\$4\text{ cm}\times4\text{ cm}\times7\text{ cm}=112\text{}$ cm}^3$.

The cylindrical hole has radius $1 $\text{}$
cm} and height equal to that of the block of wood, 7 $\text{}$ cm}$.

The volume of the cylindrical hole is thus $\$\pi\times(1\text{ cm})^2\times7\text{ cm}=7\pi\text{}$ cm}^3$.

In $\text{cm}^3$ , the volume of the
block of wood after the hole is drilled is $112-7\pi\approx90.01$ , which when rounded
to the nearest $\text{cm}^3$ , is
$90 \text{ cm}^3$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.