Two cylinders, A and B, are mathematically similar. [1] The height of B is twice the corresponding height of A. The volume of A is 13 cm 3. Find the volume of B.

The volume of cylinder B is 26cm³

Step-by-step explanation

The volume of a cylinder is expressed as πr²h.

given cylinder A and B,

Va = πra²ha ... (1)

Vb = πrb²hb ... (2)

If the height of B is twice the corresponding height of A, then hb = 2ha

Given the volume of A to be 13cm³ then;

13 = πra²ha ... (3)

Vb = πrb² (2ha) ... (4)

Since they are mathematically similar, both cylinder will have the same radius ra = rb

Dividing equation 4 into 3

13/Vb = πra²ha/2πrb²ha

since the radius are the same, they will cancel out to have;

13/Vb = 1 / 2

Vb = 26cm³