Answer:
The edge length of the cube of ice is 40 in.
The surface area of cube of ice is 9600 in².
Step-by-step explanation:
The volume of a cube of ice for an ice sculpture is 64,000 cubic inches.
a. What is the edge length of the cube of ice?
Substituting all the given values in the formula to find the edge length of cube of ice :
[tex]\begin{gathered} \qquad\longrightarrow{\sf{Volume_{(Cube)} = {(s)}^{3}}} \\ \\ \qquad\longrightarrow{\sf{64000= {(s)}^{3}}} \\ \\ \qquad\longrightarrow{\sf{s = \sqrt[3]{64000}}} \\ \\ \qquad\longrightarrow{\sf{s = \sqrt[3]{40 \times 40 \times 40}}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\purple{s = 40 \: in}}}}}\end{gathered}[/tex]
Hence, the edge length of the cube of ice is 40 in.
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b. What is the surface area of the cube of ice?
Substituting all the given values in the formula to find the surface area of cube of ice :
[tex]\begin{gathered} \qquad\longrightarrow{\sf{Surface \: Area_{(Cube)} = 6{(s)}^{2}}} \\ \\ \qquad\longrightarrow{\sf{S_{(Cube)} = 6(40)^{2} }} \\ \\ \qquad\longrightarrow{\sf{SA_{(Cube)} = 6(40 \times 40)}} \\ \\ \qquad\longrightarrow{\sf{SA_{(Cube)} = 6(1600)}} \\ \\ \qquad\longrightarrow{\sf{SA_{(Cube)} = 6 \times 1600}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\pink{SA_{(Cube)} = 9600 \: {in}^{2}}}}}}\end{gathered}[/tex]
Hence, the surface area of cube of ice is 9600 in².
[tex]\rule{300}{2.5}[/tex]
