A sphere of 10.5 cm radius is melted and cast into a cuboid of maximum volume. The total surface area of such cuboid is approximately:
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Answered by
1
"volume of sphere = (4/3)* pi * r^3
= (4/3) * pi * (10.5) ^ 3
on solving it comes 11 * 21 * 21
let l = 11, b = 21, h = 21
so S = 2 (lb + bh + hl)
=2 (11 * 21 + 21 * 21 + 21 * 11)
=2(231+441+231)
=2*903
=1806
"
Answered by
1
Find the volume of the sphere:
Volume = 4/3 πr³
Volume = 4/3 π (10.5)³ = 4851 cm³
Find the prime factors of 4851:
4851 = 3² x 7² x 11
To get the max surface area:
*Assuming the lengths must be integer
Length = 3 cm (allocate the smallest possible factor)
Breadth = 3 cm (allocate the next smallest possible factor)
Height = 11 x 7 x 7 = 539 cm (The remaining factors)
Total surface area of the cuboid:
Total Surface Area = 2 (3 x 3 + 3 x 539 + 3 x 539)
Total Surface Area = 6486 cm²
Answer: The total surface area is 6486 cm²
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