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.
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
5 answers
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
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.
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.
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