The dimensions of a cuboidal tin box are 30cm ^ 40cm ^ 50cm. Find the tin required for 20 such boxes if the cost of tin sheet is Rs 25 per square meter
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The dimensions of a cuboidal tin box are 30cm ^ 40cm ^ 50cm. Find the tin required for 20 such boxes if the cost of tin sheet is Rs 25 per square meter
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Given data :
To find : The tin required for 20 such boxes.
Solution : Let, lenght of cuboidal tin box be 30 cm and width be 40 cm and height be 50 cm.
Now, surface area of cuboidal tin box ::
⟹ surface area of cuboid
= 2 * L * W + 2 * L * H + 2 * H * W
{ where,
⟹ L = length
⟹ W = width
⟹ H = height }
⟹ surface area of cuboid
= 2 * 30 * 40 + 2 * 30 * 50 + 2 * 50 * 40
⟹ surface area of cuboid
= 60 * 40 + 60 * 50 + 100 * 40
⟹ surface area of cuboid
= 2400 + 3000 + 4000
⟹ surface area of cuboid
= 2400 + 3000 + 4000
⟹ surface area of cuboid
= 5400 + 4000
⟹ surface area of cuboid
= 9400 cm²
Here, we know,
⟹ 9400 cm² = 0.94 m²
Hence, surface area of one cuboid tin box is 0.94 m²
Now, surface area of 20 cuboidal tin boxes::
⟹ surface area of 20 cuboid
= 0.94 * 20
⟹ surface area of 20 cuboid
= 18.8 m²
Now, cost of sheet of 20 cuboidal tin boxes::
⟹ cost of sheet = 18.8 * 25
⟹ cost of sheet = Rs 470
Answer : Hence, requirement of sheet fir 20 cuboidal tin boxes is 18.8 m² and cost of sheet is Rs 470.
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Verified answer
Answer:
₹470
Step-by-step explanation:
Length of box = 30cm = 0.3 m
Breadth of box = 40cm = 0.4 m
Height of cuboid = 50cm = 0.5 m
Total surface area of cuboid = 2(lb + bh + hl)
=> T.S.A. = 2(0.3×0.4 + 0.4×0.5 + 0.5×0.3)
=> T.S.A. = 2(0.12 + 0.20 + 0.15) m²
=> T.S.A. = 2(0.47) m² = 0.94 m²
Total surface area of 20 boxes = 20 × 0.94 = 18.8 m²
Cost of tin sheet per m² = ₹25
Total cost = ₹25 × 18.8 = ₹470