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A closed box is made up of wood which is 1 cm thick. The outer dimensions of the box are 5 cm ×4 cm ×7 cm. Find the volume of the wood used.

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110 {cm}^{3}

111 {cm}^{3}

112 {cm}^{3}

113 {cm}^{3}

answer is A.

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Detailed Solution

Given,
Length of outer box = 5 cm
Breadth of outer box = 4 cm
Height of outer box = 7 cm
Volume of outer= length × breadth × height

= 5 \times 4 \times 7

= 140 {cm}^{3}

Wood box of thickness w = 1 cm
Inner Length of inner = l – 2w
= 5 – 2 x 1
= 3 cm
Breadth of inner = b–2w
= 4 – 2 x 1
= 2 cm
Height of inner = h–2w
= 7 – 2 x 1
= 5 cm
Volume of inner = length × breadth × height

= 3 \times 2 \times 5

= 30 {cm}^{3}

Volume of wood used = Volume of outer – Volume of inner

= 140 - 30

= 110 {cm}^{3}

Thus, the volume of the wood used

= 110 {cm}^{3}

Correct option is 1.

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