125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a long cuboid. What is the percentage increase in the total surface area of the cuboid over the total surface area of the cube?
Answers
Given : 125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a long cuboid.
To find : percentage increase in the total surface area of the cuboid over the total surface area of the cube
Solution:
Let say Large cube side = 5a
Volume of cube = 125a³
Surface area of cube = 6 (5a)² = 150a²
125 identical cubes are cut from it
=> volume of each cube = 125a³ /125 = a³
=> Side of each cube = a
125 cubes arranged in a row
Hence cuboid size = 125a * a * a
Surface Area = 2 ( 125a * a + 125a *a + a *a)
= 2(251a²)
= 502a²
increase in surface area = 502a² - 150a² = 352a²
% increase in Surface Area = (352a²/150a²) * 100
= 234.67 %
234.67 % increase in total Surface area of the cube
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Answer:
Given : 125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a long cuboid.
To find: percentage increase in the total surface area of the cuboid over the total surface area of the cube
Solution:
Let say Large cube side = 5a
Volume of cube = 125a³
Surface area of cube = 6 (5a)² = 150a²
125 identical cubes are cut from it
=> volume of each cube = 125a3/125 = a³
=> Side of each cube = a
125 cubes arranged in a row
Hence cuboid size = 125a* a* a
Surface Area = 2 ( 125a* a + 125a *a + a *a)
= 2(251a²)
= = 502a²
increase in surface area = = 352a² 502a² - 150a²
% increase in Surface Area = (352a²/ 150a²) * 100
= 234.67 =234.2/3