A cube whose edge measures 8 cm is cut into cubes whose edge measures 1.0 cm. Find the ratio of the

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09 Dec 2015 Cube

A cube whose edge measures 8 cm is cut into cubes whose edge measures 1.0 cm. Find the ratio of the surface area of the original cube to the sum of the surface areas of the new cubes.

OPtion

1) 1:5
2) 1:2
3) 2:5
4) 3:5
5) 1:8
6) 1:3
7) 3:4
8) 1:9
9) 3:7
10)1:6

Solution

Sum of volume of new cubes = Volume of original cube.
using this to find number of cubes, we can find ratio of surface areas.
Volume of original cube = 8^3 = 512 cm^3
Volume of new cube = 1^3 = 1 cm^3
So, number of new cubes = Volume of original cube/Volume of new cube
=512
Surface area of original cube = 6*8^2 = 384 cm^2
Surface area of new cube = 6 1^2 = 6 cm^2
total surface area of all cubes = 512*6 = 3072 cm^2
Ratio of surface area of original cube to sum of surface areas of new cube
348/3072 = 1/8
1:8
Option 5)

Correct Option: 5 Best Solution (2)

Md Shahid Akhter   9 years AGO

No. of cubes = Volume of original cube / Volume of each cube
= 8*8*8/1*1*1
= 8^3
SA of original cube / Sum of SA of new cubes =
(6*8^2)/( 8^3*6*1^2)
= 1:8

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NIKHIL JAIN   9 years AGO

Volume of Original cube= 8*8*8
volume of new cube=1*1*1
total cubes formed=8*8*8
surface area of original cube/ sum of surface areas of new cubes=
6*8*8/8*8*8*6*1*1= 1/8

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