Question

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?

The edge length of the cube of ice is
inches.

b. What is the surface area of the cube of ice?

The surface area of the cube of ice is
square inches.

Answer 1

Below!

Explanation:

We know that:

• Length = Height = Width
• Volume = LHW = L³ = 64000
• Surface area = 6(area of a square)

Part A Solution:

• L³ = 64000
• ∛L³ = ∛64000
• => L = ∛40 x 40 x 40
• => L = 40 inches

Hence, the length is 40 inches.

Part B Solution:

We know that the length is 40 units. Since this is a cube, L must equal to W.

• => L² = 6(40 x 40)
• => L² = 6(1600)
• => 9600 square inches

Hence, the surface area is 9600 square inches.

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Hoped this helped.

`BrainiacUser1357`

Answer 2

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 :

`\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 * 40 * 40}}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\purple{s = 40 \: in}}}}}\end{gathered}`

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 :

`\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 * 40)}} \\ \\ \qquad\longrightarrow{\sf{SA_((Cube)) = 6(1600)}} \\ \\ \qquad\longrightarrow{\sf{SA_((Cube)) = 6 * 1600}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\pink{SA_((Cube)) = 9600 \: {in}^(2)}}}}}\end{gathered}`

Hence, the surface area of cube of ice is 9600 in².

`\rule{300}{2.5}`