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External dimensions of a closed wooden box are in the ratio 5:4:3. If the cost of painting its outer surface at the rate of Rs 5 per dm² is Rs 11,750, find the dimensions of the box.

Solution:

The surface area of the box = 2 × (LB + BH + LH)

L = Length; B = Breadth; H = Height

Rate = Rs. 5 per dm²

Surface Area = Rs. 11,750/5 = 2350dm²

2 × (LB + BH + LH) = 2350 — (1)

We know:

L/B = 5/4

B = 4L/5 — (2)

L/H = 5/3

H = 3L/5 — (3)

Substituting (2) & (3) in (1) we get

2 × (4L²/5 + 12L²/25 + 3L²/5) = 2350

2 × (47L²/25) = 2350

L² = (2350 × 25)/(47 × 2)

L² = (50 × 25)/2

L² = 25 × 25

L = 25 dm

B = 4 × 25/5 = 20 dm

H = 3 × 25/5 = 15 dm

Hence we get the desired dimensions

✦ Try This: External dimensions of a closed wooden box are in the ratio 5:3:2. If the cost of painting its outer surface at the rate of Rs 10 per dm² is Rs 15,500, find the dimensions of the box.

The surface area of the box = 2 × (LB + BH + LH)

L = Length; B = Breadth; H = Height

Rate = Rs. 10 per dm²

Surface Area = Rs. 11,750/5 = 2350dm²

2 × (LB + BH + LH) = 1550 — (1)

We know:

L/B = 5/3

B = 3L/5 — (2)

L/H = 5/2

H = 2L/5 — (3)

Substituting (2) & (3) in (1) we get

2 × (3L²/5 + 6L²/25 + 2L²/5) = 1550

2 × (31L²/25) = 1550

L² = (1550 × 25)/(31 × 2)

L² = (50 × 25)/2

L² = 25 × 25

L = 25 dm

B = 4 × 25/5 = 20 dm

H = 3 × 25/5 = 15 dm

Hence we get the desired dimensions

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 109

External dimensions of a closed wooden box are in the ratio 5:4:3. If the cost of painting its outer surface at the rate of Rs 5 per dm² is Rs 11,750, find the dimensions of the box.

Summary:

External dimensions of a closed wooden box are in the ratio 5:4:3. If the cost of painting its outer surface at the rate of Rs 5 per dm² is Rs 11,750, the dimensions of the box L = 25dm, B = 20dm, H = 15dm

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