Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
External dimensions of a closed wooden box are in the ratio 5:4:3.
Let the external dimensions of the closed wooden box be 5x, 4x and 3x.
The cost of painting = ₹ 5 per dm2
Total cost of painting = ₹ 11750
∴ Total surface area = `"Total cost of painting"/("Cost of painting per dm"^2) = 11750/5`
Total surface area of a cuboid = 2(lb + bh + hl)
= 2(5x × 4x + 4x × 3x + 3x × 5x)
= 2(20x2 + 12x2 + 15x2)
= 2 × 47x2
= 94x2
Since, total surface area = 2350 dm2
⇒ 94x2 = 2350
⇒ `x^2 = 2350/94 = 25`
∴ x = 5
Hence, dimensions of the box are 5x × 5 = 25 dm, 4x × 5 = 20 dm and 3x × 5 = 15 dm.
APPEARS IN
संबंधित प्रश्न
Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block
covered with coloured paper with picture of Santa Claus on it. She must know the exact
quantity of paper to buy for this purpose. If the box has length, breadth and height as 80
cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would
she require?
A tea-packet measures 10 cm × 6 cm × 4 cm. How many such tea-packets can be placed in a cardboard box of dimensions 50 cm × 30 cm × 0.2 m?
The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is 12 `sqrt(3)` cm. Find the edges of three cubes.
The length, breadth, and height of a cuboid are in the ratio 6: 5 : 3. If its total surface area is 504 cm2; find its dimensions. Also, find the volume of the cuboid.
The length, breadth, and height of a cuboid (rectangular solid) are 4 : 3: 2.
(i) If its surface area is 2548 cm2, find its volume.
(ii) If its volume is 3000 m3, find its surface area.
