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A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and thickness of wood as 2.5 cm. The volume of the wood is
(a) 85,000 cm³
(b) 80,000 cm³
(c) 82,125 cm³
(d) 84,000 cm³

Solution:

The walls of the wooden box are 2.5 cm thick.

Internal volume of the box = 115 × 75 × 35 = 301,875 cm³

The thickness of walls is 2.5cm, hence the length, breadth and height becomes as follows:

Length = 115 + 2 × 2.5 = 115 + 5 = 120cm

Breadth = 75 + 2 × 2.5 = 75 + 5= 80cm

Height = 35 + 2 × 2.5 = 40 cm

The outer Volume of the wooden box is = 120 × 80 × 40 = 384,000

The Volume of the wood = Outer volume minus inner volume = 384,000 - 301,875 = 82,125

The correct choice is the answer (c )

✦ Try This: A covered wooden box has the inner measures as 117 cm, 72 cm and 32 cm and thickness of wood as 1.5 cm. The volume of the wood is (a) 65,000 cm³, (b) 45,432 cm³, (c) 54,182cm³, (d) 44,000 cm³

The walls of the wooden box are 2.5 cm thick.

Internal volume of the box = 117 × 72 × 32 = 269,568 cm³

The thickness of walls is 2.5cm, hence the length, breadth and height becomes as follows:

Length = 115 + 2 × 1.5 = 117 + 3 = 120cm

Breadth = 72 + 2 × 1.5 = 72 + 3= 75cm

Height = 32 + 2 × 1.5 = 35 cm

The outer Volume of the wooden box is = 120 × 75 × 35 = 315,000cm³

The Volume of the wood = Outer volume minus inner volume = 315,000 - 269,568 = 45,432cm³

The correct choice is the answer (b )

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 23

A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and thickness of wood as 2.5 cm. The volume of the wood is (a) 85,000 cm³ (b) 80,000 cm³ (c) 82,125 cm³ (d) 84,000 cm³

Summary:

A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and thickness of wood as 2.5 cm. The volume of the wood is 82,125 cm³

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