Question

A box is a cuboid with dimensions 29cm by 15cm by 20cm, measured to the nearest centimeter. Disc cases are cuboids measured 1.4cm by 14.2cm by 19.3cm to the nearest millimeter. Show that 19 disc cases stacked straight down will definitely fit in the box. (This is a bounds question, so please answer accordingly.)

Answer 1

The volume of the box is 8700 cm³ and the volume of one disc case is 379.684 cm³. Since the volume of the disc cases (7214.996 cm³) is less than the volume of the box, 19 disc cases will definitely fit.

Step-by-step explanation:

To determine if 19 disc cases will fit in the box, we need to compare the volumes of the disc cases and the box. The volume of a cuboid is given by multiplying its length by its width by its height. The volume of the box is 29 cm x 15 cm x 20 cm = 8700 cm³.

The volume of a disc case is 1.4 cm x 14.2 cm x 19.3 cm = 379.684 cm³. To find out if 19 disc cases will fit, we multiply the volume of one disc case by 19: 379.684 cm³ x 19 = 7214.996 cm³. Since the volume of the disc cases is less than the volume of the box, 19 disc cases will definitely fit.