Question

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

Answer 1

Answer:

$r = x\sqrt{3.54}$

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:

$Volume = \frac{1}{3}\pi r^2h$

Where h represents height and r represents radius;

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

$\frac{1}{3}\pi r^2 * x = 3.7x^3$

Multiply both sides by 3

$3 * \frac{1}{3}\pi r^2 * x = 3.7x^3 * 3$

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

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

Multiply both sides by x

$\frac{\pi r^2 * x}{x} = \frac{11.1x^3}{x}$

$\pi r^2 = \frac{11.1x^3}{x}$

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

Take π as 3.14

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

Divide both sides by 3.14

$\frac{3.14 * r^2}{3.14} = \frac{11.1x^2}{3.14}$

$r^2 = \frac{11.1x^2}{3.14}$

$r^2 = 3.54x^2$

Take Square root of both sides

$\sqrt{r^2} = \sqrt{3.54x^2}$

$r = \sqrt{3.54x^2}$

Split the square root

$r = \sqrt{3.54} * \sqrt{x^2}$

$r = \sqrt{3.54} * x$

$r = x\sqrt{3.54}$