circle rapid - fire word problems
solve each short word problem. show all formulas, substitutions, and work. round answers to the nearest tenth unless otherwise stated.
problem 1 — bike tire
a bicycle tire has a radius of 14 inches.
a. what is the circumference of the tire?
b. how far does the bike travel in 3 full rotations of the tire?
problem 2 — pepperoni slice zone
a large pepperoni slice on a pizza is perfectly circular with a diameter of 3 cm. what is the area of the pepperoni slice?
problem 3 — paint can lid
a round paint can lid has a radius of 5 cm. how much metal surface area is on the top of the lid?
problem 4 — field marker rope
a coach uses a rope to outline a circular training area with a radius of 18 ft. how many feet of rope does she need to outline the circle?
problem 5 — clock face
the circular face of a wall clock has an area of 452 square centimeters. what is the approximate radius of the clock?

Question

circle rapid - fire word problems
solve each short word problem. show all formulas, substitutions, and work. round answers to the nearest tenth unless otherwise stated.
problem 1 — bike tire
a bicycle tire has a radius of 14 inches.
 a. what is the circumference of the tire?
 b. how far does the bike travel in 3 full rotations of the tire?
problem 2 — pepperoni slice zone
a large pepperoni slice on a pizza is perfectly circular with a diameter of 3 cm. what is the area of the pepperoni slice?
problem 3 — paint can lid
a round paint can lid has a radius of 5 cm. how much metal surface area is on the top of the lid?
problem 4 — field marker rope
a coach uses a rope to outline a circular training area with a radius of 18 ft. how many feet of rope does she need to outline the circle?
problem 5 — clock face
the circular face of a wall clock has an area of 452 square centimeters. what is the approximate radius of the clock?

Accepted Answer

### Problem 1 - Bike Tire
#### Part a: Circumference of the tire
# Explanation:
## Step 1: Recall the formula for circumference of a circle
The formula for the circumference $ C $ of a circle with radius $ r $ is $ C = 2\pi r $.

## Step 2: Substitute the given radius
Given $ r = 14 $ inches. Substitute into the formula:
$ C = 2 \times \pi \times 14 $

## Step 3: Calculate the circumference
$ C = 28\pi \approx 28 \times 3.1416 \approx 87.96 $ inches. Rounding to the nearest tenth, $ C \approx 88.0 $ inches.

# Answer:
The circumference of the tire is approximately $ \boldsymbol{88.0} $ inches.

#### Part b: Distance traveled in 3 rotations
# Explanation:
## Step 1: Understand the relationship
One rotation of the tire covers a distance equal to its circumference. For 3 rotations, the distance $ d $ is $ 3 \times $ circumference.

## Step 2: Substitute the circumference from part (a)
From part (a), $ C \approx 88.0 $ inches. So, $ d = 3 \times 88.0 $

## Step 3: Calculate the distance
$ d = 264.0 $ inches.

# Answer:
The bike travels approximately $ \boldsymbol{264.0} $ inches in 3 full rotations.

### Problem 2 - Pepperoni Slice Zone
# Explanation:
## Step 1: Recall the formula for the area of a circle
The area $ A $ of a circle with radius $ r $ is $ A = \pi r^2 $. The diameter is 3 cm, so the radius $ r = \frac{\text{diameter}}{2} = \frac{3}{2} = 1.5 $ cm.

## Step 2: Substitute the radius into the area formula
$ A = \pi \times (1.5)^2 $

## Step 3: Calculate the area
$ (1.5)^2 = 2.25 $, so $ A = \pi \times 2.25 \approx 3.1416 \times 2.25 \approx 7.0686 $ cm². Rounding to the nearest tenth, $ A \approx 7.1 $ cm².

# Answer:
The area of the pepperoni slice is approximately $ \boldsymbol{7.1} $ cm².

### Problem 3 - Paint Can Lid
# Explanation:
## Step 1: Recall the formula for the area of a circle
The area $ A $ of a circle with radius $ r $ is $ A = \pi r^2 $.

## Step 2: Substitute the given radius
Given $ r = 5 $ cm. Substitute into the formula:
$ A = \pi \times (5)^2 $

## Step 3: Calculate the area
$ (5)^2 = 25 $, so $ A = 25\pi \approx 25 \times 3.1416 \approx 78.54 $ cm². Rounding to the nearest tenth, $ A \approx 78.5 $ cm².

# Answer:
The metal surface area on the top of the lid is approximately $ \boldsymbol{78.5} $ cm².

### Problem 4 - Field Marker Rope
# Explanation:
## Step 1: Recall the formula for circumference of a circle
The length of the rope needed to outline the circle is the circumference $ C $ of the circle. The formula for circumference with radius $ r $ is $ C = 2\pi r $.

## Step 2: Substitute the given radius
Given $ r = 18 $ ft. Substitute into the formula:
$ C = 2 \times \pi \times 18 $

## Step 3: Calculate the circumference
$ C = 36\pi \approx 36 \times 3.1416 \approx 113.0976 $ ft. Rounding to the nearest tenth, $ C \approx 113.1 $ ft.

# Answer:
She needs approximately $ \boldsymbol{113.1} $ feet of rope.

### Problem 5 - Clock Face
# Explanation:
## Step 1: Recall the formula for the area of a circle
The area $ A $ of a circle is $ A = \pi r^2 $. We need to solve for $ r $ given $ A = 452 $ cm².

## Step 2: Rearrange the formula to solve for $ r $
$ r^2 = \frac{A}{\pi} $, so $ r = \sqrt{\frac{A}{\pi}} $

## Step 3: Substitute the given area
Substitute $ A = 452 $ cm²:
$ r = \sqrt{\frac{452}{\pi}} $

## Step 4: Calculate the radius
First, calculate $ \frac{452}{\pi} \approx \frac{452}{3.1416} \approx 143.87 $. Then, $ r = \sqrt{143.87} \approx 11.99 $ cm. Rounding to the nearest tenth, $ r \approx 12.0 $ cm.

# Answer:
The approximate radius of the clock face is $ \boldsymbol{12.0} $ centimeters.

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QUESTION IMAGE

Question

Explanation:

Problem 1 - Bike Tire

Part a: Circumference of the tire

Step 1: Recall the formula for circumference of a circle

Step 2: Substitute the given radius

Step 3: Calculate the circumference

Step 1: Understand the relationship

Step 2: Substitute the circumference from part (a)

Step 3: Calculate the distance

Step 1: Recall the formula for the area of a circle

Step 2: Substitute the radius into the area formula

Step 3: Calculate the area

Answer:

Part b: Distance traveled in 3 rotations