There are three cylinders - C1, C2 and C3. The ratio of height and radius of these cylinders are 3 : 6 : 5 and 2 : 3 : 4 respectively, in that order of C1, C2 and C3. The valueof Einstein factor, X, is directly proportional to the lateral surface area of a cylinder and is inversely proportional to its volume. A company requires a cylinder with the lowest Einstein Factor. Which of the following cylinder(s) should the company select?a)Only C1b)Only C3c)Both C1and C3d)Both C1and C2Correct answer is option 'B'. Can you explain this answer?

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There are three cylinders - C₁, C₂ and C₃. The ratio of height and radius of these cylinders are 3 : 6 : 5 and 2 : 3 : 4 respectively, in that order of C₁, C₂and C₃. The value of Einstein factor, X, is directly proportional to the lateral surface area of a cylinder and is inversely proportional to its volume. A company requires a cylinder with the lowest Einstein Factor. Which of the following cylinder(s) should the company select?

a)
Only C₁
b)
Only C₃
c)
Both C₁ and C₃
d)
Both C₁ and C₂

Correct answer is option 'B'. Can you explain this answer?

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There are three cylinders - C1, C2 and C3. The ratio of height and rad...

Factor X is lowest for the cylinder with the highest radius, i.e. cylinder C₃.
Hence, option 2.

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There are three cylinders - C1, C2 and C3. The ratio of height and rad...

Given information:
- The ratio of height and radius of the cylinders C1, C2, and C3 is 3:6:5 and 2:3:4, respectively.
- The value of the Einstein factor, X, is directly proportional to the lateral surface area of a cylinder and inversely proportional to its volume.

To find:
The cylinder with the lowest Einstein factor.

Solution:
Let's calculate the lateral surface area and volume of each cylinder to determine the Einstein factor.

Cylinder C1:
Let the common ratio between height and radius be x.
Then, the height of C1 = 3x and the radius of C1 = 6x.

The lateral surface area of C1 = 2πrh = 2π(6x)(3x) = 36πx^2.
The volume of C1 = πr^2h = π(6x)^2(3x) = 108πx^3.

Cylinder C2:
Let the common ratio between height and radius be y.
Then, the height of C2 = 6y and the radius of C2 = 3y.

The lateral surface area of C2 = 2πrh = 2π(3y)(6y) = 36πy^2.
The volume of C2 = πr^2h = π(3y)^2(6y) = 54πy^3.

Cylinder C3:
Let the common ratio between height and radius be z.
Then, the height of C3 = 5z and the radius of C3 = 4z.

The lateral surface area of C3 = 2πrh = 2π(4z)(5z) = 40πz^2.
The volume of C3 = πr^2h = π(4z)^2(5z) = 80πz^3.

Calculating the Einstein factor:
The Einstein factor, X, is directly proportional to the lateral surface area and inversely proportional to the volume.

For cylinder C1, X1 = (36πx^2) / (108πx^3) = 1 / (3x).
For cylinder C2, X2 = (36πy^2) / (54πy^3) = 2 / (3y).
For cylinder C3, X3 = (40πz^2) / (80πz^3) = 1 / (2z).

Comparison:
To find the cylinder with the lowest Einstein factor, we need to compare the values of X for each cylinder.

- X1 = 1 / (3x)
- X2 = 2 / (3y)
- X3 = 1 / (2z)

From the given ratios, we can see that x < y="" />< />

Therefore, X1 > X2 > X3.

Hence, the company should select only Cylinder C3 as it has the lowest Einstein factor.

Answered by Wizius Careers · View profile

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There are three cylinders - C1, C2 and C3. The ratio of height and radius of these cylinders are 3 : 6 : 5 and 2 : 3 : 4 respectively, in that order of C1, C2 and C3. The valueof Einstein factor, X, is directly proportional to the lateral surface area of a cylinder and is inversely proportional to its volume. A company requires a cylinder with the lowest Einstein Factor. Which of the following cylinder(s) should the company select?a)Only C1b)Only C3c)Both C1and C3d)Both C1and C2Correct answer is option 'B'. Can you explain this answer?

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