An $8 \mathrm{~cm}$ cube has a $4 \mathrm{~cm}$ square hole cut through its centre, as shown. What is the remaining volume, in $\mathrm{cm}^{3}$ ?
(A) 64
(D) 384
(B) 128
(E) 448
(C) 256

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-144.jpg?height=395&width=458&top_left_y=686&top_left_x=1294)

## Part B: Each question is worth 6 credits.
An $8 \mathrm{~cm}$ cube has a $4 \mathrm{~cm}$ square hole cut through its centre, as shown. What is the remaining volume, in $\mathrm{cm}^{3}$ ?
(A) 64
(D) 384
(B) 128
(C) 256
(E) 448

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-268.jpg?height=450&width=523&top_left_y=1190&top_left_x=1359)

## Solution

Remaining volume $=8 \times 8 \times 8-8 \times 4 \times 4$ (in $\left.\mathrm{cm}^{3}\right)$

$$
\begin{aligned}
& =8(64-16) \\
& =8 \times 48 \\
& =384
\end{aligned}
$$

ANSWER: (D)

## Part B