Question

The outer dimensions of a wooden box are 20 cm, 12 cm and 8 cm. The thickness of the wood is 10 mm. Find (i) the volume of wood and (ii) the cost of the wood required for the box if 1 cm³ of wood costs ₹ 8.50.

Answer 1

Given:

• Outer dimensions of the wooden box:
  • Length L = 20 cm
  • Width W = 12 cm
  • Height H = 8 cm
• Thickness of the wood: 10 mm = 1 cm
• Cost of wood: ₹ 8.50 per cm³

Step 1: Calculate the volume of the wood

We will find the volume of wood by subtracting the volume of the inner box from the volume of the outer box.

1. Outer volume of the box:

The outer dimensions of the box are given, so the volume of the outer box is:

Outer volume = L × W × H

 = 20 × 12 × 8

= 1,920 cm³

2. Inner dimensions of the box:

Since the thickness of the wood is 1 cm, the inner dimensions of the box will be reduced by 2 cm in each direction (1 cm on each side). 

• Inner length = 20 – 2 = 18 cm 
• Inner width = 12 – 2 = 10 cm 
• Inner height = 8 – 2 = 6 cm 

3. Inner volume of the box:

The inner volume of the box is:

Inner volume = 18 × 10 × 6 = 1,080 cm³

4. Volume of the wood: 

The volume of the wood is the difference between the outer volume and the inner volume:

Volume of wood = Outer volume – Inner volume

= 1,920 cm³ – 1,080 cm³

= 840 cm³

Step 2: Calculate the cost of the wood

Now, we will calculate the cost of the wood based on the volume of the wood and the given cost per cm³.

Cost of the wood = Volume of wood × Cost per cm³

Cost of the wood = 840 cm³ × 8.50 = ₹ 7,140