Question

The volume of a cone is 3.7x3 cubic units and its height is x units.

Which expression represents the radius of the cone's base, in units?
3x
6x
Зах?
9.xox2​

Answer 1

`r = x√(3.54)`

Step-by-step explanation:

The options are not well presented; However, the solution is as follows

Given

Shape: Cone

`Volume = 3.7x^3`

Height = x

Required

Find the radius of the cone

The volume of a cone is:

`Volume = (1)/(3)\pi r^2h`

Where h represents height and r represents radius;

Substitute x for h and
`3.7x^3` for Volume

`(1)/(3)\pi r^2 * x = 3.7x^3`

Multiply both sides by 3

`3 * (1)/(3)\pi r^2 * x = 3.7x^3 * 3`

`\pi r^2 * x = 3.7x^3 * 3`

`\pi r^2 * x = 11.1x^3`

Multiply both sides by x

`(\pi r^2 * x)/(x) = (11.1x^3)/(x)`

`\pi r^2 = (11.1x^3)/(x)`

`\pi r^2 = 11.1x^2`

Take π as 3.14

`3.14 * r^2 = 11.1x^2`

Divide both sides by 3.14

`(3.14 * r^2)/(3.14) = (11.1x^2)/(3.14)`

`r^2 = (11.1x^2)/(3.14)`

`r^2 = 3.54x^2`

Take Square root of both sides

`√(r^2) = √(3.54x^2)`

`r = √(3.54x^2)`

Split the square root

`r = √(3.54) * √(x^2)`

`r = √(3.54) * x`

`r = x√(3.54)`