The ship has 3 circular portholes, porthole A, porthole B, and porthole C. Porthole A, the smallest of the three has a circumference of between 2pi and 6pi feet. Porthole C, the largest of the portholes, has circumference of LESS than 3 times porthole A. What is the raidus, circumference, and area for porthole A, porthole B, and porthole C

Question

The ship has 3 circular portholes, porthole A, porthole B, and porthole C. Porthole A, the smallest of the three has a circumference of between 2pi and 6pi feet. Porthole C, the largest of the portholes, has circumference of LESS than 3 times porthole A. What is the raidus, circumference, and area for porthole A, porthole B, and porthole C

Answer 1

The ship has 3 circular portholes, porthole A, porthole B, and porthole C. Porthole A, the smallest of the three has a circumference of between 2pi and 6pi feet. Porthole C, the largest of the portholes, has circumference of LESS than 3 TIMES porthole A. What is the raidus, circumference, and area for porthole A, porthole B, and porthole C

Answer 2

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Answer 3

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Answer 4

Let's assign variables to the information given. Let's call the radius of porthole A "rA", the radius of porthole B "rB", and the radius of porthole C "rC".

From the information given, we know that the circumference of porthole A is between 2π and 6π feet. Circumference of a circle can be calculated using the formula C = 2πr, where "C" is the circumference and "r" is the radius.

So, we can write the inequality as:
2πrA < C(A) < 6πrA

To find the radius, circumference, and area for each porthole, we need more information or assumptions about their relationship or specific values within the given ranges.

Answer 5

To find the radius, circumference, and area of the portholes, we'll need to use the formulas for calculating these measurements for a circle.

Let's start with porthole A, which has a circumference between 2π and 6π feet. The formula for calculating the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius.

Since we know the circumference is between 2π and 6π feet, we can write the following inequality:

2π < C < 6π

To solve this inequality, divide both sides by 2π:

1 < r < 3

So, the radius of porthole A is between 1 and 3 feet.

To find the circumference, we can choose any value within this range for the radius. Let's choose the minimum value, r = 1 foot. Substituting this in the circumference formula, we get:

C = 2π(1) = 2π feet

Therefore, porthole A has a radius of between 1 and 3 feet, with a circumference of 2π feet.

To find the area of porthole A, we can use the formula:

A = πr^2

Substituting in the minimum radius, r = 1 foot, we get:

A = π(1^2) = π square feet

So, porthole A has an area of π square feet.

Now let's move on to porthole C. We know that its circumference is less than 3 times the circumference of porthole A. Using the formula for circumference, we have:

C_c < 3C_a

where C_c is the circumference of porthole C and C_a is the circumference of porthole A.

Substituting the value for C_a (2π) we found earlier:

C_c < 3(2π)
C_c < 6π

This means that the circumference of porthole C is less than 6π feet.

To find the radius and area of porthole C, we need more information.

Answer 6

Let x be the radius of porthole A.

The circumference of porthole A is 2πx, which is between 2π and 6π. Therefore:
2π < 2πx < 6π
Dividing everything by 2π, we get:
1 < x < 3

So the radius of porthole A is between 1 and 3 feet.

Let y be the radius of porthole B. We don't have any information about porthole B, so we can't determine its radius, circumference, or area.

Let z be the radius of porthole C.

The circumference of porthole C is 2πz, which is less than 3 times the circumference of porthole A:
2πz < 3(2πx)
Dividing everything by 2π, we get:
z < 3x

Substituting x = 1 and x = 3, we get:
z < 3 (if x = 1)
z < 9 (if x = 3)

So the radius of porthole C is less than 3 feet if the radius of porthole A is 1 foot, and less than 9 feet if the radius of porthole A is 3 feet.

To summarize:
- The radius of porthole A is between 1 and 3 feet.
- We don't have enough information to determine the radius, circumference, or area of porthole B.
- The radius of porthole C is less than 3 feet if the radius of porthole A is 1 foot, and less than 9 feet if the radius of porthole A is 3 feet.

Answer 7

Let rA be the radius of porthole A and let cA be the circumference of porthole A. Since the circumference of a circle is given by c = 2πr, we have:

2πrA < cA < 6πrA

Dividing all terms by 2π, we get:

rA < cA/(2π) < 3rA

Thus, the radius of porthole A is between cA/(2π) and 3rA. We cannot determine the exact radius or circumference of porthole A without knowing the value of cA.

Let rB be the radius of porthole B, and let cB and aB represent its circumference and area, respectively. Since we have no information about porthole B, we cannot determine its radius, circumference, or area.

Let rC be the radius of porthole C and let cC be its circumference. We know that cC is less than 3 times the circumference of porthole A, or:

cC < 3cA

Since cA = 2πrA, we have:

cC < 6πrA

Dividing both sides by 2π, we have:

rC < 3rA

Thus, the radius of porthole C is less than 3 times the radius of porthole A. We cannot determine the exact radius or circumference of porthole C without knowing the value of rA, but we do know that it is less than 3rA.