Answer:
[tex]r = x\sqrt{3.54}[/tex]
Explanation:
The options are not well presented; However, the solution is as follows
Given
Shape: Cone
[tex]Volume = 3.7x^3[/tex]
Height = x
Required
Find the radius of the cone
The volume of a cone is:
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
Where h represents height and r represents radius;
Substitute x for h and [tex]3.7x^3[/tex] for Volume
[tex]\frac{1}{3}\pi r^2 * x = 3.7x^3[/tex]
Multiply both sides by 3
[tex]3 * \frac{1}{3}\pi r^2 * x = 3.7x^3 * 3[/tex]
[tex]\pi r^2 * x = 3.7x^3 * 3[/tex]
[tex]\pi r^2 * x = 11.1x^3[/tex]
Multiply both sides by x
[tex]\frac{\pi r^2 * x}{x} = \frac{11.1x^3}{x}[/tex]
[tex]\pi r^2 = \frac{11.1x^3}{x}[/tex]
[tex]\pi r^2 = 11.1x^2[/tex]
Take π as 3.14
[tex]3.14 * r^2 = 11.1x^2[/tex]
Divide both sides by 3.14
[tex]\frac{3.14 * r^2}{3.14} = \frac{11.1x^2}{3.14}[/tex]
[tex]r^2 = \frac{11.1x^2}{3.14}[/tex]
[tex]r^2 = 3.54x^2[/tex]
Take Square root of both sides
[tex]\sqrt{r^2} = \sqrt{3.54x^2}[/tex]
[tex]r = \sqrt{3.54x^2}[/tex]
Split the square root
[tex]r = \sqrt{3.54} * \sqrt{x^2}[/tex]
[tex]r = \sqrt{3.54} * x[/tex]
[tex]r = x\sqrt{3.54}[/tex]
