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_6ed09463f225f8ba1f07g-144.jpg?height=382&width=441&top_left_y=1652&top_left_x=1292)
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
(B) 128
(C) 256
(D) 384
(E) 448

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-243.jpg?height=453&width=528&top_left_y=1107&top_left_x=1357)

## Solution

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

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

ANSWER: (D)