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a 4cm edge cube is cut into small cubes each of edge 1 cm, calculate the total surface area of small cubes.Also find the ratio of total surface area of large cube to that of small cubes.
Asked by nisha_vini29 | 03 Jan, 2015, 01:14: PM
answered-by-expert Expert Answer

begin mathsize 14px style The space dimension space of space large space cube space equals space 4 space cm space cross times 4 space cm space cross times 4 space cm space space therefore The space volume space of space large space cube space equals space 4 space cross times 4 cross times 4 space equals space 64 space cm cubed space The space dimension space of space each space small space cube space equals space 1 space cm space cross times 1 space cm space cross times 1 space cm space space therefore The space volume space of space each space small space cube space equals space 1 space cross times 1 cross times 1 space equals 1 space cm cubed space therefore Total space number space of space small space cubes space equals space 64 space cm cubed space divided by 1 space cm cubed equals space 64 Surface space area space of space straight a space cube space equals space 6 straight a squared therefore Surface space area space of space large space cube space equals space 6 cross times 4 squared space equals space 6 cross times 16 space equals space 96 space cm squared Surface space area space of space each space small space cube space equals space 6 cross times 1 squared space equals space 6 cross times 1 space equals space 6 space cm squared therefore Total space surface space area space of space small space cubes space equals number space of space cubes space cross times space surface space area space of space each space small space cube space 64 space cross times space 6 space equals space 384 space cm squared Hence comma space the space ratio space of space total space surface space area space of space large space cube space to space that space of space small space cubes space equals 96 over 384 equals 1 fourth equals space 1 space colon space 4 end style

Answered by | 04 Jan, 2016, 06:13: PM

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