Question

A wooden block has dimensions $8\text{cm}\times 5\text{cm}\times 5\text{cm}.$ A square hole with dimensions $8\text{cm}\times 2\text{cm}\times 2\text{cm}$ is drilled out of its core.


What is the volume of the remaining wood?

• A. $160$ cm${}^3$
• B. $164$ cm${}^3$
• C. $168$ cm${}^3$
• D. $172$ cm${}^3$

Answer 1

The correct option is C $168$ cm${}^3$

Volume of wood used $=$ Volume of entire wooden block $-$ Volume of the hole

Entire wooden block is depicted in figure below,
Volume of entire wooden block $=8\times 5\times 5=200$ cm${}^3$

Drilled out block is shown in below figure,
Volume of hole $=$ Volume of drilled out block $=8\times 2\times 2=32$ cm${}^3$

Therefore, The volume of wood used $=200-32=168$ cm${}^3$

(c) is the correct option.