Answer:
Step-by-step explanation:
Volume of big cube with side 12 cm = Side³
= 12 ³
= 1728 cm³
Volume of 8 small cubes = Volume of big cube
8 × side³ = 1728
side³ = 1728/8
side³ = 216
Surface area of 1 small cube = 6 (a)²
= 6 (6)²
= 216 cm²
Surface area of big cube = 6 (12)²
= 864 cm²
Ratio of surace area = 216/864
Hope it helped you !!
[tex]\sf\:\boxed{\begin{aligned}& \:\sf \: Edge\:of\:new\:cube \: is \: 6 \: cm \: \\ \\& \:\sf \: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} = 4 : 1 \end{aligned}}[/tex]
Given that, a solid cube of side 12 cm is cut into 8 cubes of equal volume.
Let assume that side of new cube be x cm.
So, According to statement, we have
[tex]\sf\: Volume_{(Cube)} = 8 \times Volume_{(New\:cube)} \\ [/tex]
[tex]\sf\: {(12)}^{3} = 8 \times {x}^{3} \\ [/tex]
[tex]\sf\: {(12)}^{3} = {2}^{3} \times {x}^{3} \\ [/tex]
[tex]\sf\: {(12)}^{3} = {(2x)}^{3} \\ [/tex]
[tex]\sf\: 2x = 12 \\ [/tex]
[tex]\implies\sf\:x = 6 \: cm \\ [/tex]
Thus,
[tex]\implies\bf\:Edge\:of\:new\:cube \: is \: 6 \: cm \\ [/tex]
Now,
[tex]\sf\: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} \\ [/tex]
[tex]\sf\: = \: 6 {(12)}^{2} : 6 {(6)}^{2} \\ [/tex]
[tex]\sf\: = \: 12 \times 12 : 6 \times 6 \\ [/tex]
[tex]\sf\: = \: 2 \times 2 : 1 \times 1 \\ [/tex]
[tex]\sf\: = \: 4 : 1 \\ [/tex]
[tex]\implies\bf\: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} = 4 : 1 \\ [/tex]
Hence,
[tex]\implies\sf\:\sf\:\boxed{\begin{aligned}& \:\sf \: Edge\:of\:new\:cube \: is \: 6 \: cm \: \\ \\& \:\sf \: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} = 4 : 1 \end{aligned}}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
Formulae Used:
Let us consider a cube of side x units, then
[tex]\sf\: Volume_{(Cube)} = {x}^{3} \\ [/tex]
[tex]\sf\: Surface\:area_{(Cube)} = 6{x}^{2} \\ [/tex]
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Answers & Comments
Answer:
Side = 6 cm , Ratio = 1:4
Step-by-step explanation:
Volume of big cube with side 12 cm = Side³
= 12 ³
= 1728 cm³
Volume of 8 small cubes = Volume of big cube
8 × side³ = 1728
side³ = 1728/8
side³ = 216
side = 6 cm
Surface area of 1 small cube = 6 (a)²
= 6 (6)²
= 216 cm²
Surface area of big cube = 6 (12)²
= 864 cm²
Ratio of surace area = 216/864
= 1:4
Hope it helped you !!
Answer:
[tex]\sf\:\boxed{\begin{aligned}& \:\sf \: Edge\:of\:new\:cube \: is \: 6 \: cm \: \\ \\& \:\sf \: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} = 4 : 1 \end{aligned}}[/tex]
Step-by-step explanation:
Given that, a solid cube of side 12 cm is cut into 8 cubes of equal volume.
Let assume that side of new cube be x cm.
So, According to statement, we have
[tex]\sf\: Volume_{(Cube)} = 8 \times Volume_{(New\:cube)} \\ [/tex]
[tex]\sf\: {(12)}^{3} = 8 \times {x}^{3} \\ [/tex]
[tex]\sf\: {(12)}^{3} = {2}^{3} \times {x}^{3} \\ [/tex]
[tex]\sf\: {(12)}^{3} = {(2x)}^{3} \\ [/tex]
[tex]\sf\: 2x = 12 \\ [/tex]
[tex]\implies\sf\:x = 6 \: cm \\ [/tex]
Thus,
[tex]\implies\bf\:Edge\:of\:new\:cube \: is \: 6 \: cm \\ [/tex]
Now,
[tex]\sf\: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} \\ [/tex]
[tex]\sf\: = \: 6 {(12)}^{2} : 6 {(6)}^{2} \\ [/tex]
[tex]\sf\: = \: 12 \times 12 : 6 \times 6 \\ [/tex]
[tex]\sf\: = \: 2 \times 2 : 1 \times 1 \\ [/tex]
[tex]\sf\: = \: 4 : 1 \\ [/tex]
Thus,
[tex]\implies\bf\: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} = 4 : 1 \\ [/tex]
Hence,
[tex]\implies\sf\:\sf\:\boxed{\begin{aligned}& \:\sf \: Edge\:of\:new\:cube \: is \: 6 \: cm \: \\ \\& \:\sf \: Surface\:area_{(Cube)} : Surface\:area_{(New\:cube)} = 4 : 1 \end{aligned}}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
Formulae Used:
Let us consider a cube of side x units, then
[tex]\sf\: Volume_{(Cube)} = {x}^{3} \\ [/tex]
[tex]\sf\: Surface\:area_{(Cube)} = 6{x}^{2} \\ [/tex]