Question

Find the volume of of iron required to make an open box who external dimensions are 36 cm into 25 cm into 16.5 cm the box being 1.5 centimetre thick throughout.If 1 cubic centimetre of iron weights 8.5 grams, find the weight of the empty box in kilograms​

Answer 1

Given:

• External dimension = 36 cm by 25 cm by 16.5 cm
• Thickness = 1.5 cm
• 1 cm³ of iron = 8.5 g

To Find:

• The weight of the empty open box

Procedure to find the answer:

• Find the volume of the box with the external dimension.
• Find the volume of the box with the internal dimension.
• The difference of the volume will give us the volume of the iron used.
• Find the weight of the iron.

Find the volume of the box with the external dimension:

$\text{Dimension = 6 cm by 25 cm by 16.5 cm}$

$\text {Volume } = 36 \times 25 \times 16.5$

$\text {Volume } = 14850 \text { cm}^3$

Find the volume of the box with the internal dimension:

$\text{Length } = 36 - 1.5 - 1.5$

$\text{Length } = 33 \text { cm}$

$\text{Breadth } = 25 - 1.5 - 1.5$

$\text{Breadth } = 22 \text { cm}$

$\text{Height } = 16.5 - 1.5$

$\text{Height } = 15 \text { cm}$

$\text{ Volume } = 33 \times 22 \times 15$

$\text{ Volume } = 10890 \text { cm}^3$

Find the volume of the iron used:

$\text{Volume of the iron} = 14850 - 10890$

$\text{Volume of the iron} = 3960 \text { cm}^3$

Find the weight of the iron used:

$1 \text{ cm}^3 = 8.5 \text{ g}$

$3960 \text{ cm}^3 = 3960 \times 8.5$

$3960 \text{ cm}^3 = 33660 \text{ g}$

$3960 \text{ cm}^3 = 33.66 \text{ kg}$

Answer: The weight of the iron is 33.66 kg