i.) Volume= 343m³
L. S. A = 196m²
T. S. A = 294m²
ii.) Volume= 175.616cm³
L. S. A = 125.44cm²
T. S. A = 188.16cm²
iii.) Volume= 614125cm³
L. S. A = 28900cm²
T. S. A = 43350cm²
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Step-by-step explanation:
Let's first recall the formulae used
[tex]\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Volume_{(Cube)}= {(edge)}^{3} \qquad \: \\ \\& \qquad \:\sf \: Lateral\:surface\:area_{(Cube)}=4 {(edge)}^{2} \\ \\& \qquad \:\sf \:Total\:surface\:area_{(Cube)}=6 {(edge)}^{2} \end{aligned}} \qquad \: \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-1}}[/tex]
Given that, edge of cube, x = 7 m
Now,
[tex]\sf \: Volume_{(Cube)} = {(7)}^{3} = 343 \: {m}^{3} \\ \\ [/tex]
[tex]\sf \: Lateral\:surface\:area_{(Cube)}=4 {(7)}^{2} = 4 \times 49 = 196 \: {m}^{2} \\ \\ [/tex]
[tex]\sf \: Total\:surface\:area_{(Cube)}=6 {(7)}^{2} = 6\times 49 = 294 \: {m}^{2} \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-2}}[/tex]
Given that, edge of cube, x = 5.6 cm
[tex]\sf \: Volume_{(Cube)} = {(5.6)}^{3} = 175.616 \: {cm}^{3} \\ \\ [/tex]
[tex]\sf \: Lateral\:surface\:area_{(Cube)}=4 {(5.6)}^{2} = 4 \times 31.36 = 125.44 \: {cm}^{2} \\ \\ [/tex]
[tex]\sf \: Total\:surface\:area_{(Cube)}=6 {(5.6)}^{2} = 6\times 31.36 = 188.16 \: {cm}^{2} \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-3}}[/tex]
Given that, edge of cube, x = 8 dm 5 cm = 85 cm
[ 1 dm = 10 cm ]
[tex]\sf \: Volume_{(Cube)} = {(85)}^{3} = 614125 \: {cm}^{3} \\ \\ [/tex]
[tex]\sf \: Lateral\:surface\:area_{(Cube)}=4 {(85)}^{2} = 4 \times 7225 = 28900 \: {cm}^{2} \\ \\ [/tex]
[tex]\sf \: Total\:surface\:area_{(Cube)}=6 {(85)}^{2} = 6 \times 7225 = 43350 \: {cm}^{2} \\ \\ [/tex]
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Answers & Comments
i.) Volume= 343m³
L. S. A = 196m²
T. S. A = 294m²
ii.) Volume= 175.616cm³
L. S. A = 125.44cm²
T. S. A = 188.16cm²
iii.) Volume= 614125cm³
L. S. A = 28900cm²
T. S. A = 43350cm²
Please mark me as Brainliest
Verified answer
Step-by-step explanation:
Let's first recall the formulae used
[tex]\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Volume_{(Cube)}= {(edge)}^{3} \qquad \: \\ \\& \qquad \:\sf \: Lateral\:surface\:area_{(Cube)}=4 {(edge)}^{2} \\ \\& \qquad \:\sf \:Total\:surface\:area_{(Cube)}=6 {(edge)}^{2} \end{aligned}} \qquad \: \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-1}}[/tex]
Given that, edge of cube, x = 7 m
Now,
[tex]\sf \: Volume_{(Cube)} = {(7)}^{3} = 343 \: {m}^{3} \\ \\ [/tex]
[tex]\sf \: Lateral\:surface\:area_{(Cube)}=4 {(7)}^{2} = 4 \times 49 = 196 \: {m}^{2} \\ \\ [/tex]
[tex]\sf \: Total\:surface\:area_{(Cube)}=6 {(7)}^{2} = 6\times 49 = 294 \: {m}^{2} \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-2}}[/tex]
Given that, edge of cube, x = 5.6 cm
Now,
[tex]\sf \: Volume_{(Cube)} = {(5.6)}^{3} = 175.616 \: {cm}^{3} \\ \\ [/tex]
[tex]\sf \: Lateral\:surface\:area_{(Cube)}=4 {(5.6)}^{2} = 4 \times 31.36 = 125.44 \: {cm}^{2} \\ \\ [/tex]
[tex]\sf \: Total\:surface\:area_{(Cube)}=6 {(5.6)}^{2} = 6\times 31.36 = 188.16 \: {cm}^{2} \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-3}}[/tex]
Given that, edge of cube, x = 8 dm 5 cm = 85 cm
[ 1 dm = 10 cm ]
Now,
[tex]\sf \: Volume_{(Cube)} = {(85)}^{3} = 614125 \: {cm}^{3} \\ \\ [/tex]
[tex]\sf \: Lateral\:surface\:area_{(Cube)}=4 {(85)}^{2} = 4 \times 7225 = 28900 \: {cm}^{2} \\ \\ [/tex]
[tex]\sf \: Total\:surface\:area_{(Cube)}=6 {(85)}^{2} = 6 \times 7225 = 43350 \: {cm}^{2} \\ \\ [/tex]