Question

From a wooden block of length, breadth and height 24 cm, 12 cm and 8 cm respectively, cubes of side 3 cm are cut out. How much volume of wood is left out?

• A. 576 cm${}^3$
• B. 684 cm${}^3$
• C. 1064 cm${}^3$
• D. 854 cm${}^3$

Answer 1

The correct option is A 576 cm${}^3$

Given, length, breadth and height of the cuboid are 24 cm, 12 cm and 8 cm respectively.
Volume of cuboid $=l\times b\times h$
$=24\times 12\times 8$
$=2,304{\text{cm}}^3$
No. of cubes that can be cut along the length = $\frac{24}{3}=8$
No. of cubes that can be cut along the breadth = $\frac{12}{3}=4$
No. of cubes that can be cut along the height = $\frac{8}{3}=2.66$
= 2 (No. of cubes can't be in decimals)
So, total number of cube can be cut $=8\times 4\times 2=64$
Volume of each cube = $3\times 3\times 3$
= 27 cm${}^3$
Volume of all cubes = $27\times 64$
= 1,728 cm${}^3$
$\therefore$ Volume of wood left out is
= 2,304 - 1,728
= 576 cm${}^3$