Math / Geometry

QuestionUse the image to $V=512 \mathrm{~m}^{3} \quad V=1728 \mathrm{~m}^{3}$
The two cubes are similar in shape. Compare the volume of the two and determine the scale factor from the smaller cube to the larger cube. En fraction. (1 point) $\square$ Check answer Remaining Attempts : 3

Studdy Solution

STEP 1

What is this asking? We've got two cubes, one small and one big, and we know their volumes.
We need to figure out how much bigger the large cube is compared to the small one, and express this as a fraction. Watch out! Don't mix up the order – we want the scale factor from the smaller to the larger cube.

STEP 2

1. Find the side lengths.
2. Calculate the scale factor.

STEP 3

Alright, let's start with the smaller cube.
We know its volume is $512 \text{ m}^3$ .
The volume of a cube is side length cubed, so we can write this as $s^3 = 512$ , where $s$ is the side length.

STEP 4

To find $s$ , we need to take the cube root of both sides!
So, $s = \sqrt[3]{512}$ .
What number multiplied by itself three times gives us 512?
It's 8!
So, the side length of the smaller cube is $8$ m.

STEP 5

Now, let's tackle the larger cube.
Its volume is $1728 \text{ m}^3$ .
Using the same volume formula, we have $S^3 = 1728$ , where $S$ is the side length of the larger cube.

STEP 6

Taking the cube root of both sides gives us $S = \sqrt[3]{1728}$ .
And the cube root of 1728 is 12!
So, the side length of the larger cube is $12$ m.

STEP 7

The scale factor is the ratio of corresponding lengths in similar figures.
We want the scale factor from the smaller cube to the larger cube.
This means we divide the larger cube's side length by the smaller cube's side length.

STEP 8

So, the scale factor is $\frac{12}{8}$ .
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4.

STEP 9

Dividing 12 by 4 gives us 3, and dividing 8 by 4 gives us 2.
So, the simplified scale factor is $\frac{3}{2}$ .

STEP 10

The scale factor from the smaller cube to the larger cube is $\frac{3}{2}$ .

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QuestionUse the image to $V=512 \mathrm{~m}^{3} \quad V=1728 \mathrm{~m}^{3}$
The two cubes are similar in shape. Compare the volume of the two and determine the scale factor from the smaller cube to the larger cube. En fraction. (1 point) $\square$ Check answer Remaining Attempts : 3

Studdy Solution

STEP 1

STEP 2

1. Find the side lengths.
2. Calculate the scale factor.

STEP 3

Alright, let's start with the smaller cube.
We know its volume is $512 \text{ m}^3$ .
The volume of a cube is side length cubed, so we can write this as $s^3 = 512$ , where $s$ is the side length.

STEP 4

To find $s$ , we need to take the cube root of both sides!
So, $s = \sqrt[3]{512}$ .
What number multiplied by itself three times gives us 512?
It's 8!
So, the side length of the smaller cube is $8$ m.

STEP 5

Now, let's tackle the larger cube.
Its volume is $1728 \text{ m}^3$ .
Using the same volume formula, we have $S^3 = 1728$ , where $S$ is the side length of the larger cube.

STEP 6

Taking the cube root of both sides gives us $S = \sqrt[3]{1728}$ .
And the cube root of 1728 is 12!
So, the side length of the larger cube is $12$ m.

STEP 7

The scale factor is the ratio of corresponding lengths in similar figures.
We want the scale factor from the smaller cube to the larger cube.
This means we divide the larger cube's side length by the smaller cube's side length.

STEP 8

So, the scale factor is $\frac{12}{8}$ .
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4.

STEP 9

Dividing 12 by 4 gives us 3, and dividing 8 by 4 gives us 2.
So, the simplified scale factor is $\frac{3}{2}$ .

STEP 10

The scale factor from the smaller cube to the larger cube is $\frac{3}{2}$ .

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Studdy Solution

STEP 1

STEP 2

1. Find the side lengths.2. Calculate the scale factor.

STEP 3

Alright, let's **start** with the **smaller cube**.We know its **volume** is 512 m3512 \text{ m}^3512 m3.The **volume of a cube** is side length cubed, so we can write this as s3=512s^3 = 512s3=512, where sss is the side length.

STEP 4

To find sss, we need to take the **cube root** of both sides!So, s=5123s = \sqrt[3]{512}s=3512​.What number multiplied by itself three times gives us 512?It's **8**!So, the **side length** of the **smaller cube** is 888 m.

STEP 5

Now, let's tackle the **larger cube**.Its **volume** is 1728 m31728 \text{ m}^31728 m3.Using the same **volume formula**, we have S3=1728S^3 = 1728S3=1728, where SSS is the side length of the **larger cube**.

STEP 6

Taking the **cube root** of both sides gives us S=17283S = \sqrt[3]{1728}S=31728​.And the **cube root** of 1728 is **12**!So, the **side length** of the **larger cube** is 121212 m.

STEP 7

The **scale factor** is the ratio of corresponding lengths in similar figures.We want the scale factor *from* the smaller cube *to* the larger cube.This means we divide the **larger cube's side length** by the **smaller cube's side length**.

STEP 8

So, the **scale factor** is 128\frac{12}{8}812​.We can **simplify** this fraction by dividing both the **numerator** and the **denominator** by their **greatest common factor**, which is 4.

STEP 9

Dividing 12 by 4 gives us 3, and dividing 8 by 4 gives us 2.So, the **simplified scale factor** is 32\frac{3}{2}23​.

STEP 10

The scale factor from the smaller cube to the larger cube is 32\frac{3}{2}23​.

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Start learning now

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

1. Find the side lengths.
2. Calculate the scale factor.

Alright, let's start with the smaller cube.
We know its volume is $512 \text{ m}^3$ .
The volume of a cube is side length cubed, so we can write this as $s^3 = 512$ , where $s$ is the side length.

To find $s$ , we need to take the cube root of both sides!
So, $s = \sqrt[3]{512}$ .
What number multiplied by itself three times gives us 512?
It's 8!
So, the side length of the smaller cube is $8$ m.

Now, let's tackle the larger cube.
Its volume is $1728 \text{ m}^3$ .
Using the same volume formula, we have $S^3 = 1728$ , where $S$ is the side length of the larger cube.

Taking the cube root of both sides gives us $S = \sqrt[3]{1728}$ .
And the cube root of 1728 is 12!
So, the side length of the larger cube is $12$ m.

The scale factor is the ratio of corresponding lengths in similar figures.
We want the scale factor from the smaller cube to the larger cube.
This means we divide the larger cube's side length by the smaller cube's side length.

So, the scale factor is $\frac{12}{8}$ .
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4.

Dividing 12 by 4 gives us 3, and dividing 8 by 4 gives us 2.
So, the simplified scale factor is $\frac{3}{2}$ .

The scale factor from the smaller cube to the larger cube is $\frac{3}{2}$ .