Math / Geometry

QuestionA piece of wire is used to form the framework of a cube. The volume of the cube is 2,744 cubic inches. Find the length of the wire. (Hint: A cube has 12 edges)

Studdy Solution

STEP 1

What is this asking? We're figuring out how long a piece of wire needs to be if we want to bend it into the shape of a cube with a given volume. Watch out! Don't mix up volume and edge length!
We're given the volume, and we need the edge length to find the total wire length.

STEP 2

1. Find the edge length
2. Calculate the total wire length

STEP 3

Alright, let's decode this cube!
We know the volume of a cube is given by $\text{Volume} = \text{edge} \cdot \text{edge} \cdot \text{edge} = \text{edge}^3$ .
We're given that the volume is $\text{2,744 cubic inches}$ .

STEP 4

So, we have $\text{edge}^3 = 2744$ .
To find the edge length, we need to take the cube root of both sides!
Think of it like this: what number, multiplied by itself three times, equals $2744$ ?

STEP 5

$\text{edge} = \sqrt[3]{2744} = 14$ So, the edge length of our cube is $\text{14 inches}$ !

STEP 6

Now, picture bending that wire into a cube.
A cube has 12 edges, and each edge has the length we just found.

STEP 7

To get the total wire length, we simply multiply the number of edges by the length of each edge.
It's like adding up all the sides!

STEP 8

$\text{Total wire length} = 12 \cdot \text{edge} = 12 \cdot 14 = 168$

STEP 9

The wire needs to be $\text{168 inches}$ long!

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QuestionA piece of wire is used to form the framework of a cube. The volume of the cube is 2,744 cubic inches. Find the length of the wire. (Hint: A cube has 12 edges)

Studdy Solution

STEP 1

What is this asking? We're figuring out how long a piece of wire needs to be if we want to bend it into the shape of a cube with a given volume. Watch out! Don't mix up volume and edge length!
We're given the volume, and we need the edge length to find the total wire length.

STEP 2

1. Find the edge length
2. Calculate the total wire length

STEP 3

Alright, let's decode this cube!
We know the volume of a cube is given by $\text{Volume} = \text{edge} \cdot \text{edge} \cdot \text{edge} = \text{edge}^3$ .
We're given that the volume is $\text{2,744 cubic inches}$ .

STEP 4

So, we have $\text{edge}^3 = 2744$ .
To find the edge length, we need to take the cube root of both sides!
Think of it like this: what number, multiplied by itself three times, equals $2744$ ?

STEP 5

$\text{edge} = \sqrt[3]{2744} = 14$ So, the edge length of our cube is $\text{14 inches}$ !

STEP 6

Now, picture bending that wire into a cube.
A cube has 12 edges, and each edge has the length we just found.

STEP 7

To get the total wire length, we simply multiply the number of edges by the length of each edge.
It's like adding up all the sides!

STEP 8

$\text{Total wire length} = 12 \cdot \text{edge} = 12 \cdot 14 = 168$

STEP 9

The wire needs to be $\text{168 inches}$ long!

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QuestionA piece of wire is used to form the framework of a cube. The volume of the cube is 2,744 cubic inches. Find the length of the wire. (Hint: A cube has 12 edges)

Studdy Solution

STEP 1

What is this asking? We're figuring out how long a piece of wire needs to be if we want to bend it into the shape of a cube with a given volume. Watch out! Don't mix up volume and edge length!We're given the *volume*, and we need the *edge length* to find the total wire length.

STEP 2

1. Find the edge length2. Calculate the total wire length

STEP 3

STEP 4

So, we have edge3=2744 \text{edge}^3 = 2744 edge3=2744.To find the **edge length**, we need to take the *cube root* of both sides!Think of it like this: what number, multiplied by itself three times, equals 274427442744?

STEP 5

edge=27443=14 \text{edge} = \sqrt[3]{2744} = 14 edge=32744​=14 So, the **edge length** of our cube is 14 inches\text{14 inches}14 inches!

STEP 6

Now, picture bending that wire into a cube.A cube has **12 edges**, and each edge has the length we just found.

STEP 7

To get the **total wire length**, we simply multiply the number of edges by the length of each edge.It's like adding up all the sides!

STEP 8

Total wire length=12⋅edge=12⋅14=168 \text{Total wire length} = 12 \cdot \text{edge} = 12 \cdot 14 = 168 Total wire length=12⋅edge=12⋅14=168

STEP 9

The wire needs to be 168 inches\text{168 inches}168 inches long!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We're figuring out how long a piece of wire needs to be if we want to bend it into the shape of a cube with a given volume. Watch out! Don't mix up volume and edge length!
We're given the volume, and we need the edge length to find the total wire length.

1. Find the edge length
2. Calculate the total wire length

So, we have $\text{edge}^3 = 2744$ .
To find the edge length, we need to take the cube root of both sides!
Think of it like this: what number, multiplied by itself three times, equals $2744$ ?

$\text{edge} = \sqrt[3]{2744} = 14$ So, the edge length of our cube is $\text{14 inches}$ !

Now, picture bending that wire into a cube.
A cube has 12 edges, and each edge has the length we just found.

To get the total wire length, we simply multiply the number of edges by the length of each edge.
It's like adding up all the sides!

$\text{Total wire length} = 12 \cdot \text{edge} = 12 \cdot 14 = 168$

The wire needs to be $\text{168 inches}$ long!