Question

The outer dimensions of a Closed wooden box are 10cm by 8cm by 7cm . Thickness of the wood is 1 cm. Find the Total cost of wood required to make box, if 1 cm³ of wood costs Rs, 2.00.​

Answer 1

Answer:

The outer dimension of Closed window is 10cm;8cm;7cm

Width of wooden box is 1cm

The inner dimensions are given by 8cm;6cm;5cm

The volume occupied by Wooden box is given by Volume of box with outer dimensions-Volume of box with inner dimensions10×8×7−8×6×5560−240320cm3

Cost of 1cm3 is 2Rs.

Cost of 320cm3 is 2×320=640Rs.

Answer 2

Question :-

• The outer dimensions of a Closed wooden box are 10cm by 8cm by 7cm . Thickness of the wood is 1 cm. Find the Total cost of wood required to make box, if 1 cm³ of wood costs Rs, 2.00.

Given :-

The External Dimension of box :-

• Length = 10cm
• Breadth = 8cm
• Height = 7cm
• Thickness = 1cm
• Cost of 1cm³ = Rs, 2.00

To Find :-

• Total cost of wood required to make box.

Solution :-

$\qquad \quad {:} \longrightarrow \sf \boxed{\tt{Volume \: of \: the \: box \: = \: Length \: \times \: Breadth \: \times \: Height }}$

$\qquad \quad {:} \longrightarrow \sf {{ External \: volume \:of \: box \: = \: (10\: \times \:8 \: \times \: 7) {cm}^{3} }}$

$\quad \sf { \bf{ ➳\: External \: volume \:of \: box \: = \: 560 {cm}^{3} }}$

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Internal Dimensions of box :-

• Internal Length = 10 - 2 = 8cm
• Internal Breadth = 8 - 2 = 6cm
• Internal Height = 7 - 2 = 5cm

$\qquad \quad {:} \longrightarrow \sf {{ Internal \: volume \:of \: box \: = \: (8\: \times \:6\: \times \: 5) {cm}^{3} }}$

$\quad \sf { \bf{ ➳\:Internal \: volume \:of \: box \: = \: 240 {cm}^{3} }}$

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$\qquad \quad {:} \longrightarrow \sf \boxed{\tt{Volume \: of \: the \: Wood\: = \: External \: Volume \: - \: Internal \: Volume }}$

$\qquad \quad {:} \longrightarrow \sf {{Volume \: of \: the \: Wood\: = \: 560 \: - \: 240 }}$

$\quad \sf { \bf{ ➳\: Volume \: of \: the \: Wood \: = \: 320{cm}^{3} }}$

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$\qquad \quad {:} \longrightarrow \sf \boxed{\tt{Cost \: of \: Wood \: = \: Volume\: of \: wood \: \times \: 2 }}$

$\qquad \quad {:} \longrightarrow \sf {{Cost \: of \: Wood\: = \: 320\: \times \: 2 }}$

$\quad \sf { \bf{ ➳\:Cost \: of \: the \: Wood \: = \: Rs, 640 }}$

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$\begin{gathered}\begin{gathered} \therefore\: \sf{ Cost \: of \: Wood \: required \: for \: box \: = \underline {\underline{Rs, 640}}}\\\end{gathered}\end{gathered}$

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