A cuboidal oil tin is 30cm*40cm*50cm. Find the cost of the tin required for making 20 such tins if the cost of tin sheet is Rs. 20/m2.

AnswEr:

The cost of the tins depend upon their total surface area . It is given that a tin is in the shape of a cuboid such that

• Length l = 30 cm
• Breadth b = 40 cm
• Height h = 50 cm

[tex]\star[/tex] Surface area of one tin :

[tex] = \sf \: 2(lb + bh + hl) \\ \\ \sf = 2(30 \times 40 + 40 \times 50 + 30 \times 50) {cm}^{2} \\ \\ = \sf2(1200 + 2000 + 1500) {cm}^{2} \\ \\ = \sf(2 \times 4700) {cm}^{2} = 9400 \: {cm}^{2} \\ \\ [/tex]

[tex]\therefore[/tex] Surface area of 20 such tins :

[tex]\sf{(2\times\:9400)cm^2}[/tex]

[tex] \implies \sf \: 188000 \: {cm}^{2} \\ \\[/tex]

Now, we have to convert cm into m.

[tex] \implies \sf \dfrac{188000}{10000} \: {m}^{2} \\ \\ \implies \sf 18.8 \: {m}^{2} [/tex]

______________________

Now,

Cost of 1 sq. m of tin sheet = Rs 20

[tex]\therefore[/tex] Cost of 18.8 m² of tin sheet = [tex]\sf{20\times\:18.8}=Rs\:376[/tex]

Hence, the cost of making 20 tins = Rs 376

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