Math, asked by smitamoholesm, 7 months ago

A cube of dimensions 10" is painted red, blue and green respectively, on the three sets of opposite
faces. The cube is then cut into 104 smaller cubes, some with 4” dimensions and some with 2"
dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The
remaining cubes of dimensions 4" have only one of their faces painted green.
How many smaller cubes have at least one of their faces painted blue ?​

Answers

Answered by amitnrw
8

Given : A cube of dimensions 10" is painted red, blue and green respectively, on the three sets of opposite  faces. The cube is then cut into 104 smaller cubes, some with 4” dimensions and some with 2"

dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The  remaining cubes of dimensions 4" have only one of their faces painted green.

To Find :  How many smaller cubes have at least one of their faces painted blue ?​

Solution:

smaller cubes with 4” dimensions = a

Volume = 64a

smaller cubes with 2” dimensions = 104-a

Volume = 8*(104 - a)   =  832 - 8a

Total Volume = 10 * 10 * 10  = 1000

64a + 832 - 8a   = 1000

=> 56a  = 168

=> a = 3

cubes of dimensions 4"  = 3  

2 are  painted Red

1 is painted Green

No 4''  on Blue

Hence Blue Painted are only 2''

2'' cubes on one face = 10 * 10 / 2 * 2  =  25

on 2 Faces = 2 * 25 = 50

50 smaller cubes have at least one of their faces painted blue

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Answered by Sanidhyaa05
0

Answer:

50

Step-by-step explanation:

Given : A cube of dimensions 10" is painted red, blue and green respectively, on the three sets of opposite  faces. The cube is then cut into 104 smaller cubes, some with 4” dimensions and some with 2"

dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The  remaining cubes of dimensions 4" have only one of their faces painted green.

To Find :  How many smaller cubes have at least one of their faces painted blue ?​

Solution:

smaller cubes with 4” dimensions = a

Volume = 64a

smaller cubes with 2” dimensions = 104-a

Volume = 8*(104 - a)   =  832 - 8a

Total Volume = 10 * 10 * 10  = 1000

64a + 832 - 8a   = 1000

=> 56a  = 168

=> a = 3

cubes of dimensions 4"  = 3  

2 are  painted Red

1 is painted Green

No 4''  on Blue

Hence Blue Painted are only 2''

2'' cubes on one face = 10 * 10 / 2 * 2  =  25

on 2 Faces = 2 * 25 = 44

50 smaller cubes have at least one of their faces painted blue

plz mark as brainliast

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