Question

The volume of a cylinder, V(h), is given by the area of the base times the height, h. The base of the cylinder shown below has a diameter of 5 inches.
Part A: Write the function, V(h), that represents the volume of the cylinder

Part B: find V(3) and tell what it represents

Answer 1

Answer:

Part a) $V(h)=6.25\pi h\ in^3$

Part b) $V(3)=18.75\pi\ in^3$  (see the explanation)

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

$V=Bh$

where

B is the area of the base of cylinder

h is the height of the cylinder

we have that

$B=\pi r^{2}$

Part a) Write the function, V(h), that represents the volume of the cylinder

we have

$r=5/2=2.5\ in$ ----> the radius is half the diameter

substitute

$B=\pi (2.5)^{2}$

$B=6.25\pi\ in^2$

The volume is

$V(h)=6.25\pi h\ in^3$

Part b) Find V(3) and tell what it represents

V(3) represent the volume of the cylinder with a height of 3 inches

so

For h=3 in

substitute

$V(3)=6.25\pi(3)\ in^3$

$V(3)=18.75\pi\ in^3$