The volume of a cuboidal block of silver is 10368 cm3. If its dimensions are in the ratio 3 :2 :1, find the dimensions of the block and the cost of gold polishing its entire surface at rupees 0.50 per cm2
Answers
Answer:
Answer :-
i) Dimensions of Cuboid :-
• Length, l = 36 cm
• Breadth, b = 24 cm
• Height, h = 12 cm
ii) Cost of Polishing entire surface
= ₹ 1584
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★ Concept :-
Here the concept of Volume and Total surface area of Cuboid are used.
=> Volume = l × b × h
=> Total Surface Area = 2(lb+bh+lh)
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★ Solution :-
Given,
» The dimensions of cuboid are in ratio of 3:2:1
» Volume of cuboid = 10368 cm³
Then,
▶Let the length (l) of the cuboid be 3x
▶Let the breadth (b) of the cuboid be 2x
▶Let the height (h) of the cuboid be 1x
where x is the constant by which all teh dimensions are multiplied.
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By applying the length, breadth and height in the formula of Volume, we get,
✒ Volume = length × breadth × height
✒ 3x × 2x × 1x = 10368
✒ 6x³ = 10368
✒ x³ = 10368/6 = 1728
✒ x = ³√1728 = 12
Hence, x = 12 .
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By applying the value of x, in length, breadth and height, we get,
▶ Length, l = 3x = 3(12) = 36 cm
▶Breadth, b = 2x = 2(12) = 24 cm
▶Height, h = 1x = 1(12) = 12 cm
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In order to find the total cost of polishing we must multiply the total area to be painted with the rate of painting an area.
☞ Total Cost = Area to be painted × Rate
Let us find the area to be painted. In order to find the area to be painted, we must take total surface area of solid.
→ T.S.A. = 2(lb + bh + lh)
→ T.S.A. = 2(36×24 + 24×12 + 36×12)
→ T.S.A. = 2(864 + 288 + 432)
→ T.S.A. = 2 × 1584
→ T.S.A. = 3168 cm²
Hence, we get total surface to be painted = 3168 cm².
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• Rate of Painting per area = ₹ 0.50 per cm²
Then,
✏ Total Cost of Painting = 3168 × 0.5
✏ Total Cost of Painting = ₹ 1584
Hence, we get the total cost of painting the cuboid = ₹ 1584.
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★ More to know :-
• Volume of Cube = (Side)³
• Volume of cylinder = πr²h
• Volume of Sphere = 4/3 (πr³)
• Volume of cone = ⅓(πr²h)