Math / Geometry

QuestionWhat is the surface area of this sphere? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\square$ square feet

Studdy Solution

STEP 1

What is this asking? We need to find the total surface area of a sphere, basically how much wrapping paper we'd need to perfectly cover a ball. Watch out! Don't confuse the formula for surface area with the formula for volume!
We're dealing with area here, not how much space it takes up.

STEP 2

1. Recall the formula
2. Plug and chug

STEP 3

Alright, let's kick things off with the formula for the surface area of a sphere.
Drumroll please... it's $A = 4 \cdot \pi \cdot r^2$ !
Remember, $A$ stands for the surface area, and $r$ is the radius of our sphere.
This formula tells us how much area covers the entire surface of the sphere.

STEP 4

Now, let's plug in our radius, which is $\text{radius} = r = 6.2$ feet.
So, we have $A = 4 \cdot \pi \cdot (6.2)^2$ .

STEP 5

Next, we square the radius: $(6.2)^2 = 6.2 \cdot 6.2 = 38.44$ .
Remember, squaring a number means multiplying it by itself!
So, our formula becomes $A = 4 \cdot \pi \cdot 38.44$ .

STEP 6

We're given that we should use $\pi \approx 3.14$ .
Let's substitute that in: $A = 4 \cdot 3.14 \cdot 38.44$ .

STEP 7

Now, let's multiply those numbers together: $4 \cdot 3.14 = 12.56$ .
So, we have $A = 12.56 \cdot 38.44$ .

STEP 8

Finally, multiplying $12.56$ by $38.44$ gives us $A \approx 482.81$ .

STEP 9

Remember, we need to round our answer to the nearest hundredth.
Since our answer is already to the hundredths place, our final answer is $482.81$ square feet.

STEP 10

The surface area of the sphere is approximately $482.81$ square feet.

Was this helpful?

QuestionWhat is the surface area of this sphere? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\square$ square feet

Studdy Solution

STEP 1

What is this asking? We need to find the total surface area of a sphere, basically how much wrapping paper we'd need to perfectly cover a ball. Watch out! Don't confuse the formula for surface area with the formula for volume!
We're dealing with area here, not how much space it takes up.

STEP 2

1. Recall the formula
2. Plug and chug

STEP 3

Alright, let's kick things off with the formula for the surface area of a sphere.
Drumroll please... it's $A = 4 \cdot \pi \cdot r^2$ !
Remember, $A$ stands for the surface area, and $r$ is the radius of our sphere.
This formula tells us how much area covers the entire surface of the sphere.

STEP 4

Now, let's plug in our radius, which is $\text{radius} = r = 6.2$ feet.
So, we have $A = 4 \cdot \pi \cdot (6.2)^2$ .

STEP 5

Next, we square the radius: $(6.2)^2 = 6.2 \cdot 6.2 = 38.44$ .
Remember, squaring a number means multiplying it by itself!
So, our formula becomes $A = 4 \cdot \pi \cdot 38.44$ .

STEP 6

We're given that we should use $\pi \approx 3.14$ .
Let's substitute that in: $A = 4 \cdot 3.14 \cdot 38.44$ .

STEP 7

Now, let's multiply those numbers together: $4 \cdot 3.14 = 12.56$ .
So, we have $A = 12.56 \cdot 38.44$ .

STEP 8

Finally, multiplying $12.56$ by $38.44$ gives us $A \approx 482.81$ .

STEP 9

Remember, we need to round our answer to the nearest hundredth.
Since our answer is already to the hundredths place, our final answer is $482.81$ square feet.

STEP 10

The surface area of the sphere is approximately $482.81$ square feet.

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.

QuestionWhat is the surface area of this sphere? Use π≈3.14\pi \approx 3.14π≈3.14 and round your answer to the nearest hundredth. □\square□ square feet

Studdy Solution

STEP 1

What is this asking? We need to find the total surface area of a sphere, basically how much wrapping paper we'd need to perfectly cover a ball. Watch out! Don't confuse the formula for surface area with the formula for volume!We're dealing with area here, not how much space it takes up.

STEP 2

1. Recall the formula2. Plug and chug

STEP 3

STEP 4

Now, let's **plug in** our **radius**, which is radius=r=6.2\text{radius} = r = 6.2radius=r=6.2 feet.So, we have A=4⋅π⋅(6.2)2A = 4 \cdot \pi \cdot (6.2)^2A=4⋅π⋅(6.2)2.

STEP 5

Next, we **square** the **radius**: (6.2)2=6.2⋅6.2=38.44(6.2)^2 = 6.2 \cdot 6.2 = 38.44(6.2)2=6.2⋅6.2=38.44.Remember, squaring a number means multiplying it by itself!So, our formula becomes A=4⋅π⋅38.44A = 4 \cdot \pi \cdot 38.44A=4⋅π⋅38.44.

STEP 6

We're given that we should use π≈3.14\pi \approx 3.14π≈3.14.Let's **substitute** that in: A=4⋅3.14⋅38.44A = 4 \cdot 3.14 \cdot 38.44A=4⋅3.14⋅38.44.

STEP 7

Now, let's **multiply** those numbers together: 4⋅3.14=12.564 \cdot 3.14 = 12.564⋅3.14=12.56.So, we have A=12.56⋅38.44A = 12.56 \cdot 38.44A=12.56⋅38.44.

STEP 8

Finally, **multiplying** 12.5612.5612.56 by 38.4438.4438.44 gives us A≈482.81A \approx 482.81A≈482.81.

STEP 9

Remember, we need to round our answer to the nearest hundredth.Since our answer is already to the hundredths place, our **final answer** is 482.81482.81482.81 square feet.

STEP 10

The surface area of the sphere is approximately 482.81482.81482.81 square feet.

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.

QuestionWhat is the surface area of this sphere? Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\square$ square feet

What is this asking? We need to find the total surface area of a sphere, basically how much wrapping paper we'd need to perfectly cover a ball. Watch out! Don't confuse the formula for surface area with the formula for volume!
We're dealing with area here, not how much space it takes up.

1. Recall the formula
2. Plug and chug

Now, let's plug in our radius, which is $\text{radius} = r = 6.2$ feet.
So, we have $A = 4 \cdot \pi \cdot (6.2)^2$ .

Next, we square the radius: $(6.2)^2 = 6.2 \cdot 6.2 = 38.44$ .
Remember, squaring a number means multiplying it by itself!
So, our formula becomes $A = 4 \cdot \pi \cdot 38.44$ .

We're given that we should use $\pi \approx 3.14$ .
Let's substitute that in: $A = 4 \cdot 3.14 \cdot 38.44$ .

Now, let's multiply those numbers together: $4 \cdot 3.14 = 12.56$ .
So, we have $A = 12.56 \cdot 38.44$ .

Finally, multiplying $12.56$ by $38.44$ gives us $A \approx 482.81$ .

Remember, we need to round our answer to the nearest hundredth.
Since our answer is already to the hundredths place, our final answer is $482.81$ square feet.

The surface area of the sphere is approximately $482.81$ square feet.