radical equations

Question

The volume of a cone of sand moved by harvester ants given it's radius can be found with the following formula r=3√3V/2πr A mound of gravel is in the shape of a cone with the height equal to twice the radius. Calculate the volume of such a mound of gravel whose radius is 3.5 ft. Use π=3.14

 

V=

Answer 1

Lets assume that your formula is to be used to solve the problem. If so, then when solving for v in the equation lets perform the following operations:

multiply both sides by 2πr result: 2πr²=3√3v

solve for v

v=(2πr² )/3√3

rationalize the denominator of the right side of the equation

v=(2πr² )∗√3/3√3∗√3

simplifies to:v=(2πr² )∗√3/9

Substitute for Pi=3.14 and the radius =3.5

v=(2∗3.14∗3.15² √3)/9

v=11.99

note:using your formula.