Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45 millimeters. How much water can Micah fill in his cup?

Micah can put 61072.56 ml³ of water in his cup.

Step-by-step explanation:

The volume of a cone is given by the following formula:

In which h is the height and r is the radius.

The radius is half the diameter.

In this question:

Radius of 72/2 = 36 ml. So

Height of 45 ml, so

The dimensions are in ml, so the volume will be in ml³.

So

Micah can put 61072.56 ml³ of water in his cup.

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)