What is the volume of a box that measures 1 yard by 2 feet by 1.5 feet in cubic feet and cubic metres?

Answer 1

The volume of the box is 36 * 24 * 18 = 15552 cubic inches.

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1 ft = 1/3 yd

→ volume = 1 yd × 2 ft × 1.5 ft

= 1 yd × (2 × 1/3) yd × (1.5 × 1/3) yd

= 1/3 cu yd

= 0.333... cu yd

≈ 0.33 cu yd

1 yd = 0.9144 m (exactly)*

→ 1 cu yd = 1 yd × 1 yd × 1 yd = 0.9144 m × 0.9144 m × 0.9144 m = (0.9144)³ cu m

→ 1/3 cu yd = 1/3 × (0.9144)³ cu m

= 497757069/1953125000 cu m

= 0.25485.... cu m

≈ 0.25 cu m

* derivation of 1 yd = 0.9144m (exactly):

1 in = 2.54 cm = 0.0254 m (exactly)

1 yd = 36 in = 36 × 0.0254 m = 0.9144 m (exactly)

If you are using an approximation for 1 inch in centimetres, then

1 yd ≈ 36 × approximation ÷ 100 metres.

eg if 1 in ≈ 2.5 cm, then

1 yd ≈ 36 × 2.5 ÷ 100 m = 0.9 m

and volume ≈ 1/3 × (9/10)³ cu m = 243/1000 cu m = 0.243 cu m