Math / Geometry

Question8. Brent wants to dig a circular pond surrounded by a flower bed as shown in the following diagram. The pond will have a diameter of 10 ft and the diameter of the pond and flower bed combined will be 14 ft . a) Brent needs to know the area of the pond in order to purchase a cover for the winter. What is the area of the pond, to the nearest square foot? b) Brent needs to know the area of the flower bed to plan the layout and order the flowers. What is the area of the flower bed, to the nearest square foot?

Studdy Solution

STEP 1

What is this asking? We need to find the area of a circular pond and the area of the surrounding flower bed, given their diameters. Watch out! Don't mix up radius and diameter!
Also, make sure to subtract the pond's area from the total area to find the flower bed's area.

STEP 2

1. Find the pond's area
2. Find the combined area
3. Find the flower bed's area

STEP 3

Alright, let's dive in!
We know the pond's diameter is $\text{10 ft}$ , but the area formula uses the radius.
Remember, the radius is half the diameter.

STEP 4

So, the pond's radius is $10 \text{ ft} / 2 = \textbf{5 ft}$ .

STEP 5

Now, we can use the circle area formula: $A = \pi \cdot r^2$ .
Let's plug in our radius: $A = \pi \cdot (5 \text{ ft})^2 = \pi \cdot 25 \text{ ft}^2$ .

STEP 6

Calculating this gives us $A \approx \textbf{78.54 ft}^2$ .
Rounding to the nearest square foot, we get $\textbf{79 ft}^2$ .
The pond's area is approximately $\textbf{79 ft}^2$ !

STEP 7

Now, for the combined area of the pond and flower bed!
The combined diameter is $\text{14 ft}$ , so the radius is $14 \text{ ft} / 2 = \textbf{7 ft}$ .

STEP 8

Using the same circle area formula, $A = \pi \cdot r^2$ , we get $A = \pi \cdot (7 \text{ ft})^2 = \pi \cdot 49 \text{ ft}^2$ .

STEP 9

Calculating this gives us $A \approx \textbf{153.94 ft}^2$ .
Rounding to the nearest square foot, the combined area is approximately $\textbf{154 ft}^2$ .

STEP 10

Almost there!
To find the flower bed's area, we subtract the pond's area from the combined area.

STEP 11

So, $154 \text{ ft}^2 - 79 \text{ ft}^2 = \textbf{75 ft}^2$ .

STEP 12

a) The pond's area is approximately $\textbf{79 ft}^2$ . b) The flower bed's area is approximately $\textbf{75 ft}^2$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the area of a circular pond and the area of the surrounding flower bed, given their diameters. Watch out! Don't mix up radius and diameter!
Also, make sure to subtract the pond's area from the total area to find the flower bed's area.

STEP 2

1. Find the pond's area
2. Find the combined area
3. Find the flower bed's area

STEP 3

Alright, let's dive in!
We know the pond's diameter is $\text{10 ft}$ , but the area formula uses the radius.
Remember, the radius is half the diameter.

STEP 4

So, the pond's radius is $10 \text{ ft} / 2 = \textbf{5 ft}$ .

STEP 5

Now, we can use the circle area formula: $A = \pi \cdot r^2$ .
Let's plug in our radius: $A = \pi \cdot (5 \text{ ft})^2 = \pi \cdot 25 \text{ ft}^2$ .

STEP 6

Calculating this gives us $A \approx \textbf{78.54 ft}^2$ .
Rounding to the nearest square foot, we get $\textbf{79 ft}^2$ .
The pond's area is approximately $\textbf{79 ft}^2$ !

STEP 7

Now, for the combined area of the pond and flower bed!
The combined diameter is $\text{14 ft}$ , so the radius is $14 \text{ ft} / 2 = \textbf{7 ft}$ .

STEP 8

Using the same circle area formula, $A = \pi \cdot r^2$ , we get $A = \pi \cdot (7 \text{ ft})^2 = \pi \cdot 49 \text{ ft}^2$ .

STEP 9

Calculating this gives us $A \approx \textbf{153.94 ft}^2$ .
Rounding to the nearest square foot, the combined area is approximately $\textbf{154 ft}^2$ .

STEP 10

Almost there!
To find the flower bed's area, we subtract the pond's area from the combined area.

STEP 11

So, $154 \text{ ft}^2 - 79 \text{ ft}^2 = \textbf{75 ft}^2$ .

STEP 12

a) The pond's area is approximately $\textbf{79 ft}^2$ . b) The flower bed's area is approximately $\textbf{75 ft}^2$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the area of a circular pond and the area of the surrounding flower bed, given their diameters. Watch out! Don't mix up radius and diameter!Also, make sure to subtract the pond's area from the total area to find the flower bed's area.

STEP 2

1. Find the pond's area2. Find the combined area3. Find the flower bed's area

STEP 3

Alright, let's **dive in**!We know the pond's *diameter* is 10 ft\text{10 ft}10 ft, but the area formula uses the *radius*.Remember, the radius is *half* the diameter.

STEP 4

So, the pond's radius is 10 ft/2=5 ft10 \text{ ft} / 2 = \textbf{5 ft}10 ft/2=5 ft.

STEP 5

Now, we can use the **circle area formula**: A=π⋅r2A = \pi \cdot r^2A=π⋅r2.Let's plug in our **radius**: A=π⋅(5 ft)2=π⋅25 ft2A = \pi \cdot (5 \text{ ft})^2 = \pi \cdot 25 \text{ ft}^2A=π⋅(5 ft)2=π⋅25 ft2.

STEP 6

Calculating this gives us A≈78.54 ft2A \approx \textbf{78.54 ft}^2A≈78.54 ft2.Rounding to the nearest square foot, we get 79 ft2\textbf{79 ft}^279 ft2.The pond's area is approximately 79 ft2\textbf{79 ft}^279 ft2!

STEP 7

Now, for the combined area of the pond *and* flower bed!The combined diameter is 14 ft\text{14 ft}14 ft, so the radius is 14 ft/2=7 ft14 \text{ ft} / 2 = \textbf{7 ft}14 ft/2=7 ft.

STEP 8

Using the same **circle area formula**, A=π⋅r2A = \pi \cdot r^2A=π⋅r2, we get A=π⋅(7 ft)2=π⋅49 ft2A = \pi \cdot (7 \text{ ft})^2 = \pi \cdot 49 \text{ ft}^2A=π⋅(7 ft)2=π⋅49 ft2.

STEP 9

Calculating this gives us A≈153.94 ft2A \approx \textbf{153.94 ft}^2A≈153.94 ft2.Rounding to the nearest square foot, the combined area is approximately 154 ft2\textbf{154 ft}^2154 ft2.

STEP 10

Almost there!To find the flower bed's area, we **subtract** the pond's area from the combined area.

STEP 11

So, 154 ft2−79 ft2=75 ft2154 \text{ ft}^2 - 79 \text{ ft}^2 = \textbf{75 ft}^2154 ft2−79 ft2=75 ft2.

STEP 12

a) The pond's area is approximately 79 ft2\textbf{79 ft}^279 ft2. b) The flower bed's area is approximately 75 ft2\textbf{75 ft}^275 ft2.

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 need to find the area of a circular pond and the area of the surrounding flower bed, given their diameters. Watch out! Don't mix up radius and diameter!
Also, make sure to subtract the pond's area from the total area to find the flower bed's area.

1. Find the pond's area
2. Find the combined area
3. Find the flower bed's area

Alright, let's dive in!
We know the pond's diameter is $\text{10 ft}$ , but the area formula uses the radius.
Remember, the radius is half the diameter.

So, the pond's radius is $10 \text{ ft} / 2 = \textbf{5 ft}$ .

Now, we can use the circle area formula: $A = \pi \cdot r^2$ .
Let's plug in our radius: $A = \pi \cdot (5 \text{ ft})^2 = \pi \cdot 25 \text{ ft}^2$ .

Calculating this gives us $A \approx \textbf{78.54 ft}^2$ .
Rounding to the nearest square foot, we get $\textbf{79 ft}^2$ .
The pond's area is approximately $\textbf{79 ft}^2$ !

Now, for the combined area of the pond and flower bed!
The combined diameter is $\text{14 ft}$ , so the radius is $14 \text{ ft} / 2 = \textbf{7 ft}$ .

Using the same circle area formula, $A = \pi \cdot r^2$ , we get $A = \pi \cdot (7 \text{ ft})^2 = \pi \cdot 49 \text{ ft}^2$ .

Calculating this gives us $A \approx \textbf{153.94 ft}^2$ .
Rounding to the nearest square foot, the combined area is approximately $\textbf{154 ft}^2$ .

Almost there!
To find the flower bed's area, we subtract the pond's area from the combined area.

So, $154 \text{ ft}^2 - 79 \text{ ft}^2 = \textbf{75 ft}^2$ .

a) The pond's area is approximately $\textbf{79 ft}^2$ . b) The flower bed's area is approximately $\textbf{75 ft}^2$ .