A cylinder's height is 5cm longer than the radias of its base. Write a función modeling the cylinder's volume in terms of its diameter.
radius ---- x
height ---- x+5
V = π r^2 h
= π(x^2)(x+5) , but x = d/2
= π(d^2/4)(d/2 + 5)
= π( d^3/8 + d^2/4)
or
= (1/8)π(d^3 + 2d^2)
or
= (1/8)π d^2(d + 2)
or
....
To write a function modeling the cylinder's volume in terms of its diameter, we need to express the height and radius of the cylinder in terms of its diameter.
Let's say the radius of the base is denoted by "r". According to the given information, the height is 5cm longer than the radius. Therefore, the height can be expressed as "r + 5".
Now, let's express the radius in terms of the diameter. The radius is half the diameter, so we can write the radius as "d/2".
Finally, we can write the function to calculate the volume of the cylinder using the formula for the volume of a cylinder: V = π * r^2 * h.
Substituting the expressions for the radius and height, we get:
V = π * (d/2)^2 * (r + 5)
Simplifying further, we have:
V = π * (d^2/4) * (r + 5)
And that is our function modeling the cylinder's volume in terms of its diameter.