A class is finding the radii of 3 cylinders.
Cylinder A has a surface area of 4,163.64 in.2 .
Cylinder B has a surface area of 4,521.60 in.2 .
Cylinder C has a surface area of 3,165.12 in.2 .
If the height of each cylinder is 22 inches, find the radius of each cylinder. Use 3.14 for π .
(1 point)
Responses
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 18 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 18 inches.
Cylinder A’s radius is 18 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 17 inches.
Cylinder A’s radius is 18 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 17 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 18 inches, and cylinder C’s radius is 14 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 18 inches, and cylinder C’s radius is 14 inches.
Cylinder A’s radius is 18 inches, cylinder B’s radius is 17 inches, and cylinder C’s radius is 14 inches.
Cylinder A’s radius is 18 inches, cylinder B’s radius is 17 inches, and cylinder C’s radius is 14 inches.
Skip to navigation
9 answers
Given:
Surface area = 2πr(r + h)
For Cylinder A:
4,163.64 = 2*3.14*r(r + 22)
2,081.82 = 3.14*r(r + 22)
2,081.82 = 3.14r^2 + 68.68r
3.14r^2 + 68.68r - 2,081.82 = 0
We can use the quadratic formula to solve for r:
r = (-68.68 ± sqrt(68.68^2 - 4*3.14*(-2081.82))) / (2*3.14)
r ≈ 17 inches (rounded to the nearest whole number)
For Cylinder B:
4,521.60 = 2*3.14*r(r + 22)
2,260.80 = 3.14r(r + 22)
2,260.80 = 3.14r^2 + 68.68r
3.14r^2 + 68.68r - 2,260.80 = 0
Solving the quadratic equation for Cylinder B:
r ≈ 14 inches (rounded to the nearest whole number)
For Cylinder C:
3,165.12 = 2*3.14*r(r + 22)
1,582.56 = 3.14r(r + 22)
1,582.56 = 3.14r^2 + 68.68r
3.14r^2 + 68.68r - 1,582.56 = 0
Solving the quadratic equation for Cylinder C:
r ≈ 16 inches (rounded to the nearest whole number)
Therefore, the correct values are:
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 16 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 16 inches.
Given:
Surface area of Cylinder A = 4,163.64 in^2
Surface area of Cylinder B = 4,521.60 in^2
Surface area of Cylinder C = 3,165.12 in^2
Height (h) of all cylinders = 22 inches
The formula for the surface area of a cylinder is: 2πr^2 + 2πrh
Using the given values:
For Cylinder A:
4,163.64 = 2*3.14*r^2 + 2*3.14*r*22
4,163.64 = 6.28r^2 + 138.16r
6.28r^2 + 138.16r - 4,163.64 = 0
Using the quadratic formula to solve for r, we get r ≈ 17 inches
For Cylinder B:
4,521.60 = 2*3.14*r^2 + 2*3.14*r*22
4,521.60 = 6.28r^2 + 138.16r
6.28r^2 + 138.16r - 4,521.60 = 0
Solving this equation, we get r ≈ 14 inches
For Cylinder C:
3,165.12 = 2*3.14*r^2 + 2*3.14*r*22
3,165.12 = 6.28r^2 + 138.16r
6.28r^2 + 138.16r - 3,165.12 = 0
Solving this equation, we get r ≈ 16 inches
Therefore, the correct answer is:
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 16 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 18 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 18 inches.
Cylinder A’s radius is 18 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 17 inches.
Cylinder A’s radius is 18 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 17 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 18 inches, and cylinder C’s radius is 14 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 18 inches, and cylinder C’s radius is 14 inches.
Cylinder A’s radius is 18 inches, cylinder B’s radius is 17 inches, and cylinder C’s radius is 14 inches.
Cylinder A’s radius is 17 inches, cylinder B’s radius is 14 inches, and cylinder C’s radius is 18 inches.
1 answer