The outer dimensions of a closed wooden box o | vedclass

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Question

(A) External dimensions are $l = 12 	ext{ cm}, b = 10 	ext{ cm}, h = 8 	ext{ cm}$.External volume $= 12 	ext{ cm} 	imes 10 	ext{ cm} 	imes 8

Vedclass · Accepted Answer

$1440$

Vedclass · Answer

(A) External dimensions are $l = 12 	ext{ cm}, b = 10 	ext{ cm}, h = 8 	ext{ cm}$.External volume $= 12 	ext{ cm} 	imes 10 	ext{ cm} 	imes 8 	ext{ cm} = 960 	ext{ cm}^3$.Since the box is $1 	ext{ cm}$ thick,the internal dimensions are calculated by subtracting $2 	imes 	ext{thickness}$ from each dimension:Internal length $= 12 - 2(1) = 10 	ext{ cm}$.Internal breadth $= 10 - 2(1) = 8 	ext{ cm}$.Internal height $= 8 - 2(1) = 6 	ext{ cm}$.Internal volume $= 10 	ext{ cm} 	imes 8 	ext{ cm} 	imes 6 	ext{ cm} = 480 	ext{ cm}^3$.Volume of wood used $= 	ext{External volume} - 	ext{Internal volume} = 960 	ext{ cm}^3 - 480 	ext{ cm}^3 = 480 	ext{ cm}^3$.Cost of wood $= 480 	ext{ cm}^3 	imes ₹ 3.00/	ext{cm}^3 = ₹ 1440$.

The outer dimensions of a closed wooden box of $1 \text{ cm}$ thickness are $12 \text{ cm} \times 10 \text{ cm} \times 8 \text{ cm}$. Find the cost of the wood required to make the box if $1 \text{ cm}^3$ of wood costs $₹ 3.00$.

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