Question

determine the radius of the cone ,if the voulime of the cone is 125 cm to the power of 3 and the height of the cone is 12cm. Round your anwser to thenearest hundredth

Answer 1

For this case we have that by definition, the volume of a cone is given by:

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

Where:

r: It is the radius of the cone

h: It is the height of the cone

According to the statement data we have:

$h = 12 \ cm\\V = 125 \ cm ^ 3$

Substituting in the formula:

$125 = \frac {1} {3} * \pi * r ^ 2 * 12$

We cleared the radius:

$3 * 125 = \pi * r ^ 2 * 12\\\frac {3 * 125} {12 \pi} = r ^ 2\\9.9522 = r ^ 2\\r = \pm \sqrt {9.9522}$

We choose the positive value:

$r = 3.1547$

We round and we have that the radius of the cone is:

$r = 3.16 \ cm$

ANswer:

$r = 3.16 \ cm$