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A wooden box (including the lid) has external dimensions 40 cm by 34 cm by 30 cm. If the wood is 1 cm thick, how many cm³ of wood is used in it?

Solution:

The external dimensions of the wooden box are 40 cm by 34 cm by 30

Since the thickness of the wood is 1 cm the inner dimensions of the box will be:

(40 - 2)cm by (34 - 2)cm by (30 - 2)cm

= 38cm by 32 cm by 28 cm.

The amount of wood in cm³ used to construct the box is calculated as shown below:

Outer Volume - Inner volume = (40 × 34 × 30) - (38 × 32 × 28) cm³

= 40800 - 34048

= 6752cm³

The amount of wood used in the box is 6752cm³

✦ Try This: A wooden box (including the lid) has external dimensions 90 cm by 60 cm by 45 cm. If the wood is 1.5 cm thick, how many cm³ of wood is used in it?

The external dimensions of the wooden box are 90 cm by 60 cm by 45

Since the thickness of the wood is 1.5 cm the inner dimensions of the box will be:

(90 - 3)cm by (60 - 3) cm by (45 - 3)cm

= 87cm by 57 cm by 42 cm.

The amount of wood in cm³ used to construct the box is calculated as shown below:

Outer Volume - Inner volume = (90 × 60 × 45) - (87 × 57 × 42) cm³

= 243,000 - 208,278

= 34,722cm³

The amount of wood used in the box is 34,722cm³

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 98

A wooden box (including the lid) has external dimensions 40 cm by 34 cm by 30 cm. If the wood is 1 cm thick, how many cm³ of wood is used in it?

Summary:

A wooden box (including the lid) has external dimensions 40 cm by 34 cm by 30 cm. If the wood is 1 cm thick, then 6752 cm³ of wood is used in it

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