Answer:
The lateral surface area of the cube will be 36 cm²
Step-by-step explanation:
The volume of the cube is given to be 27 cm³
We will first find the measure of side of the cube
volume of cube = (side)³
27 = (side)³
side = 3 cm
lateral surface area = 4a²
= 4 × (3)²
= 4 × 9
= 36 cm²
❒ Question :-
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❒ Answer :-
❒ Explanation :-
● First, we will find measure of side :-
[tex] \dag \: \: \sf{Volume \: of \: cube = (side)^{3} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{27 \: = \: (side) {}^{3} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{side \: = \sqrt[3]{ \: 27 \: } } \\ [/tex]
[tex] \Longrightarrow \: \: \sf {side \: = \: 3 \: cm } \\ [/tex]
● Now, let's find Lateral Surface Area :-
[tex] \dag \: \: \sf{Lateral \: Surface \: Area = 4 \: {a}^{2} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{Lateral \: Surface \: Area = 4 \times ({3})^{2} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{Lateral \: Surface \: Area = 3 \times 9} \\ [/tex]
[tex] \Longrightarrow \: \: \sf{Lateral \: Surface \: Area = {36 \: cm}^{2}} \\ [/tex]
Hence :-
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[tex] \begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \pmb {\sf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \sf{Volume = ( \: edge \: ) {}^{3} } \\ \\ \\ \footnotesize \bigstar \: \sf{Total \: Surface \: Area = 6 \times ( \: edge \: ) {}^{2} } \\ \\ \\ \footnotesize \bigstar \: \sf{Lateral \: Surface \: Area = 4 \times ( \: edge \: ) {}^{2} } \\ \\ \\ \footnotesize \bigstar \: \sf{Diagonal = ( \: edge \: \sqrt{3} \: )}\end{array}}\end{gathered}\end{gathered} [/tex]
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Answers & Comments
Answer:
The lateral surface area of the cube will be 36 cm²
Step-by-step explanation:
The volume of the cube is given to be 27 cm³
We will first find the measure of side of the cube
volume of cube = (side)³
27 = (side)³
side = 3 cm
lateral surface area = 4a²
= 4 × (3)²
= 4 × 9
= 36 cm²
❒ Question :-
⠀⠀⠀⠀⠀⠀⠀
❒ Answer :-
⠀⠀⠀⠀⠀⠀⠀
❒ Explanation :-
⠀⠀⠀⠀⠀⠀⠀
● First, we will find measure of side :-
[tex] \dag \: \: \sf{Volume \: of \: cube = (side)^{3} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{27 \: = \: (side) {}^{3} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{side \: = \sqrt[3]{ \: 27 \: } } \\ [/tex]
[tex] \Longrightarrow \: \: \sf {side \: = \: 3 \: cm } \\ [/tex]
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● Now, let's find Lateral Surface Area :-
[tex] \dag \: \: \sf{Lateral \: Surface \: Area = 4 \: {a}^{2} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{Lateral \: Surface \: Area = 4 \times ({3})^{2} } \\ [/tex]
[tex] \Longrightarrow \: \: \sf{Lateral \: Surface \: Area = 3 \times 9} \\ [/tex]
[tex] \Longrightarrow \: \: \sf{Lateral \: Surface \: Area = {36 \: cm}^{2}} \\ [/tex]
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Hence :-
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[tex] \begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \pmb {\sf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \sf{Volume = ( \: edge \: ) {}^{3} } \\ \\ \\ \footnotesize \bigstar \: \sf{Total \: Surface \: Area = 6 \times ( \: edge \: ) {}^{2} } \\ \\ \\ \footnotesize \bigstar \: \sf{Lateral \: Surface \: Area = 4 \times ( \: edge \: ) {}^{2} } \\ \\ \\ \footnotesize \bigstar \: \sf{Diagonal = ( \: edge \: \sqrt{3} \: )}\end{array}}\end{gathered}\end{gathered} [/tex]