Question

For two cylinders A and B the ratio of length of A to that of B is 3:1 and ratio of the diameter of A of that of B is 1:2 . Calculate the ratio of volume of A to that of B

Answer 1

Answer:

Step-by-step explanation

given,

Diameter ratio of cylinder a & b = 1:2

Length (height) ratio of cylinder a & b = 3:1

To find,

Volume ratio of cylinder a & b.

Solution,

Let,

The diameter of cylinder a = 1r

And,the diameter of cylinder b = 2r

The length of cylinder a = 3h

And,the length of cylinder b = h

(Here,h & r are assumed as variables.)

Now,

The radius of cylinder a = 1r/2

The radius of cylinder b = 2r/2 = r

T

he volume of cylinder a = π × (1r/2)² × 3h = π × 1r²/4 × 3h = 3πr²h/4

The volume of cylinder b = π × (r)² × h = πr²h

Ratio of volume = 3πr²h/4 : πr²h = 3πr²h/4 × 1/πr²h = 3/4 = 3:4

Answer 2

Answer:

Frankly based on the given data in question, we found that the ratio of the volume of A to that of B is 3:4

Step-by-step explanation:

Let the length and diameter of cylinder A be 3x and d, respectively. Let the length and diameter of cylinder B be x and 2d, respectively.

• Calculate the volume of cylinder A:
• The formula for the volume of a cylinder is given by V = πr²h, where r is the radius of the base of the cylinder and h is the height or length of the cylinder.
• Here the radius of the base of cylinder A is d/2, and the height or length of cylinder A is 3x. Therefore, the volume of cylinder A is:
• VA = π(d/2)² * 3x
• Simplifying this expression, we get:
• VA = (3/4)πd²x
• Calculate the volume of cylinder B:
• Similarly the radius of the base of cylinder B is 2d/2 = d and the height or length of cylinder B is x. Therefore, the volume of cylinder B is:
• VB = πd²x
• Calculate the ratio of the volumes of A to B:
• To find the ratio of the volumes of A to B, we divide the volume of A by the volume of B:
• VA/VB = (3/4)πd²x / πd²x
• Simplifying this expression, we get:
• VA/VB = 3/4

Therefore the ratio of the volume of A to that of B is 3:4

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