The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at 12 per m² and with paper at the rate of 13.50 per m² is ₹ 1,248. Find the dimensions of the box.
Mensuration
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Question

The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at 12 per m² and with paper at the rate of 13.50 per m² is ₹ 1,248. Find the dimensions of the box.

Mensuration

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KnowledgeBoat · Accepted Answer

Given: The ratio of dimensions of the rectangular box = 4 : 2 : 3 Let the dimension be 4a, 2a and 3a. Total surface area of box = 2(lb \+ bh \+ hl) = 2(4a x 2a \+ 2a x 3a \+ 3a x 4a) = 2(8a2 \+ 6a2 \+ 12a2) = 2 x 26a2 = 52a2 The difference between cost of covering it with paper at 12 per m2 and with paper at the rate of 13.50 per m2 = ₹ 1,248 ⇒ Total surface area x 13.5 per m2 \- Total surface area x 12 per m2 = ₹ 1,248 ⇒ 52a2 x 13.5 \- 52a2 x 12 = ₹ 1,248 ⇒ 52a2 (13.5 \- 12) = ₹ 1,248 ⇒ 52a2 x 1.5 = ₹ 1,248 ⇒ 78a2 = ₹ 1,248 ⇒ a2 = ⇒ a2 = 16 ⇒ a = ⇒ a = 4 m So, the dimensions are 4a, 2a and 3a = 4 x 4 m, 2 x 4 m and 3 x 4 m = 16 m, 8 m and 12 m Hence, the dimensions of the box are 16 m , 8 m and 12 m.

Mathematics

The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at 12 per m² and with paper at the rate of 13.50 per m² is ₹ 1,248. Find the dimensions of the box.

Mensuration

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Mathematics

The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at 12 per m2 and with paper at the rate of 13.50 per m2 is ₹ 1,248. Find the dimensions of the box.

Mensuration

Related Questions

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The dimensions of a car petrol tank are 50 cm x 32 cm x 24 cm, which is full of petrol. If a car's average consumption is 15 km per litre, find the maximum distance that can be covered by the car.

The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at 12 per m² and with paper at the rate of 13.50 per m² is ₹ 1,248. Find the dimensions of the box.

The dimensions of a solid metallic cuboid are 72 cm x 30 cm x 75 cm. It is melted and recast into identical solid metal cubes with each of edge 6 cm. Find the number of cubes formed.
Also, find the cost of polishing the surfaces of all the cubes formed at the rate ₹ 150 per sq.m.