Question

a and b are two cylinders that are mathematically similar. the area of the cross section of cylinder a is 18cm2

Answer 1

Given that cylinder A and B are mathematically similar, the volume of cylinder B is 720
`cm^3`

How to calculate volume of a cylinder

Since the cylinders A and B are mathematically similar, their corresponding dimensions are proportional.

The ratio of their heights is given as 5:10, which simplifies to 1:2.

We are given that the area of the cross-section of cylinder A is 18
`cm^2`. Let's denote the radius of cylinder A as
`r_A`. The formula for the area of the cross-section of a cylinder is A = π
`r^2`.

Given that
`A_A` = 18
`cm^2`, we can solve for
`r_A`:

`A_A` = π
`r^2`
`_A`

18 = π
`r^2`
`_A`

`r^2`
`_A` = 18/π

`r_A` = √(18/π)

Now, find the volume of cylinder B using the corresponding dimensions. Let's denote the radius of cylinder B as
`r_B` and its height as
`h_B`.

Since the volume of a cylinder is given by V = π
`r^2`h, and the cylinders A and B are mathematically similar, their volumes are proportional to the cube of their corresponding dimensions.

The ratio of their volumes is
`(h_B/h_A)^3 = (10/5)^3 = 2^3 = 8.`

Therefore, the volume of cylinder B is 8 times the volume of cylinder A.

`V_B` = 8 *
`V_A`

`V_B` = 8 * (π
`r^2`
`_A`
`h_A`)

`V_B` = 8 * (π * (18/π) * 5)

`V_B` = 8 * (18 * 5)

`V_B` = 720
`cm^3`

Therefore, the volume of cylinder B is 720
`cm^3`

A and B are two cylinders that are mathematically similar. The area of the cross-section of cylinder A is 18cm^2. The height of cylinder A is 5cm while height of cylinder B is 10cm

Work out the volume of cylinder B.