Math / Geometry

QuestionWhat is the volume of this sphere? Use $\pi \approx 3.14$ and round your answer to the nearest hundred $\square$ cubic millimeters

Studdy Solution

STEP 1

What is this asking? We need to find how much space this sphere takes up, given its radius. Watch out! Don't mix up the formulas for area and volume!
We're dealing with volume here, which is 3D!

STEP 2

1. Recall the formula
2. Plug and chug

STEP 3

Alright, let's kick things off by remembering the super important formula for the volume of a sphere.
It's $V = \frac{4}{3} \cdot \pi \cdot r^3$ , where $V$ stands for volume and $r$ is the radius.
Remember, the radius is the distance from the center of the sphere to any point on its surface!

STEP 4

Now, let's plug in the given value for the radius, which is $r = 3$ mm.
So, we have $V = \frac{4}{3} \cdot \pi \cdot (3 \text{ mm})^3$ .

STEP 5

Let's replace $\pi$ with its approximate value of $3.14$ .
So, we get $V = \frac{4}{3} \cdot 3.14 \cdot (3 \text{ mm})^3$ .

STEP 6

Time to deal with that exponent! $(3 \text{ mm})^3$ means $3 \text{ mm} \cdot 3 \text{ mm} \cdot 3 \text{ mm}$ , which equals $27 \text{ mm}^3$ .
So, our formula becomes $V = \frac{4}{3} \cdot 3.14 \cdot 27 \text{ mm}^3$ .

STEP 7

Let's multiply those numbers! $4 \cdot 3.14 \cdot 27 = 339.12$ .
So, we have $V = \frac{339.12}{3} \text{ mm}^3$ .

STEP 8

Now, let's divide $339.12$ by $3$ .
We get $V \approx 113.04 \text{ mm}^3$ .

STEP 9

Finally, we need to round our answer to the nearest hundred.
Since $113.04$ is closer to $100$ than to $200$ , our final answer is approximately $100 \text{ mm}^3$ .

STEP 10

The volume of the sphere is approximately $100$ cubic millimeters.

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QuestionWhat is the volume of this sphere? Use $\pi \approx 3.14$ and round your answer to the nearest hundred $\square$ cubic millimeters

Studdy Solution

STEP 1

What is this asking? We need to find how much space this sphere takes up, given its radius. Watch out! Don't mix up the formulas for area and volume!
We're dealing with volume here, which is 3D!

STEP 2

1. Recall the formula
2. Plug and chug

STEP 3

Alright, let's kick things off by remembering the super important formula for the volume of a sphere.
It's $V = \frac{4}{3} \cdot \pi \cdot r^3$ , where $V$ stands for volume and $r$ is the radius.
Remember, the radius is the distance from the center of the sphere to any point on its surface!

STEP 4

Now, let's plug in the given value for the radius, which is $r = 3$ mm.
So, we have $V = \frac{4}{3} \cdot \pi \cdot (3 \text{ mm})^3$ .

STEP 5

Let's replace $\pi$ with its approximate value of $3.14$ .
So, we get $V = \frac{4}{3} \cdot 3.14 \cdot (3 \text{ mm})^3$ .

STEP 6

Time to deal with that exponent! $(3 \text{ mm})^3$ means $3 \text{ mm} \cdot 3 \text{ mm} \cdot 3 \text{ mm}$ , which equals $27 \text{ mm}^3$ .
So, our formula becomes $V = \frac{4}{3} \cdot 3.14 \cdot 27 \text{ mm}^3$ .

STEP 7

Let's multiply those numbers! $4 \cdot 3.14 \cdot 27 = 339.12$ .
So, we have $V = \frac{339.12}{3} \text{ mm}^3$ .

STEP 8

Now, let's divide $339.12$ by $3$ .
We get $V \approx 113.04 \text{ mm}^3$ .

STEP 9

Finally, we need to round our answer to the nearest hundred.
Since $113.04$ is closer to $100$ than to $200$ , our final answer is approximately $100 \text{ mm}^3$ .

STEP 10

The volume of the sphere is approximately $100$ cubic millimeters.

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QuestionWhat is the volume of this sphere? Use π≈3.14\pi \approx 3.14π≈3.14 and round your answer to the nearest hundred □\square□ cubic millimeters

Studdy Solution

STEP 1

What is this asking? We need to find how much space this sphere takes up, given its radius. Watch out! Don't mix up the formulas for area and volume!We're dealing with *volume* here, which is 3D!

STEP 2

1. Recall the formula2. Plug and chug

STEP 3

STEP 4

Now, let's **plug in** the given value for the radius, which is r=3r = 3r=3 mm.So, we have V=43⋅π⋅(3 mm)3V = \frac{4}{3} \cdot \pi \cdot (3 \text{ mm})^3V=34​⋅π⋅(3 mm)3.

STEP 5

Let's **replace** π\piπ with its approximate value of 3.143.143.14.So, we get V=43⋅3.14⋅(3 mm)3V = \frac{4}{3} \cdot 3.14 \cdot (3 \text{ mm})^3V=34​⋅3.14⋅(3 mm)3.

STEP 6

STEP 7

Let's **multiply** those numbers! 4⋅3.14⋅27=339.124 \cdot 3.14 \cdot 27 = 339.124⋅3.14⋅27=339.12.So, we have V=339.123 mm3V = \frac{339.12}{3} \text{ mm}^3V=3339.12​ mm3.

STEP 8

Now, let's **divide** 339.12339.12339.12 by 333.We get V≈113.04 mm3V \approx 113.04 \text{ mm}^3V≈113.04 mm3.

STEP 9

Finally, we need to **round** our answer to the nearest hundred.Since 113.04113.04113.04 is closer to 100100100 than to 200200200, our **final answer** is approximately 100 mm3100 \text{ mm}^3100 mm3.

STEP 10

The volume of the sphere is approximately 100100100 cubic millimeters.

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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.

QuestionWhat is the volume of this sphere? Use $\pi \approx 3.14$ and round your answer to the nearest hundred $\square$ cubic millimeters

What is this asking? We need to find how much space this sphere takes up, given its radius. Watch out! Don't mix up the formulas for area and volume!
We're dealing with volume here, which is 3D!

1. Recall the formula
2. Plug and chug

Now, let's plug in the given value for the radius, which is $r = 3$ mm.
So, we have $V = \frac{4}{3} \cdot \pi \cdot (3 \text{ mm})^3$ .

Let's replace $\pi$ with its approximate value of $3.14$ .
So, we get $V = \frac{4}{3} \cdot 3.14 \cdot (3 \text{ mm})^3$ .

Let's multiply those numbers! $4 \cdot 3.14 \cdot 27 = 339.12$ .
So, we have $V = \frac{339.12}{3} \text{ mm}^3$ .

Now, let's divide $339.12$ by $3$ .
We get $V \approx 113.04 \text{ mm}^3$ .

Finally, we need to round our answer to the nearest hundred.
Since $113.04$ is closer to $100$ than to $200$ , our final answer is approximately $100 \text{ mm}^3$ .

The volume of the sphere is approximately $100$ cubic millimeters.