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Ratan Rana
Asked: 2022-11-08T13:19:31+05:30 In:

The edges of a wooden box are in the ratio 1 : 2 : 3 and its volume is 750 cm3. The cost of painting of wooden box is Rs. 21 per cm2. Find the total cost of painting the outer side of the wooden box.
1. Rs. 11500
2. Rs. 12500
3. Rs, 11550
4. Rs. 11150

The edges of a wooden box are in the ratio 1 : 2 : 3 and its volume is 750 cm3. The cost of painting of wooden box is Rs. 21 per cm2. Find the total cost of painting the outer side of the wooden box.
1. Rs. 11500
2. Rs. 12500
3. Rs, 11550
4. Rs. 11150
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  1. Correct Answer – Option 3 : Rs, 11550

    Given:
    Ratio of sides of the wooden box = 1 : 2 : 3
    Volume of the wooden box = 750 cm3
    Rate of painting = Rs. 21 per cm2

    Concept used:
    Total surface area of cuboidal box = 2 × (lb + bh + hl)
    Volume of cuboidal box = l × b × h
    Cost of painting the cuboidal box = Rate × Total surface area of box

    Calculation:
    Let sides of the box be a, 2a and 3a.
    Volume of box = 750
    ⇒ a × 2a × 3a = 750
    ⇒ 6a3 = 750
    ⇒ a3 = 750/6
    ⇒ a3 = 125
    ⇒ a = 5
    Surface area of box = 2(a × 2a + 2a × 3a + 3a × a)
    ⇒ 2(2a2 + 6a2 + 3a2)
    ⇒ 2 × 11a2
    ⇒ 22 × 5 × 5
    ⇒ 550 cm2
    Cost of painting = 21 × 550
    ⇒ Rs. 11550
    ∴ The cost of painting the outer side of the wooden box is Rs. 11550.

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