Exercise 37 Page 723

The volume of the remaining solid will be the difference between the volumes of the total cylinder and the cylinder cut out. Let's recall the formula for the volume of a cylinder. V= π r^2 h Let's start by finding the volume of the total cylinder. We are given the diameter of 6 centimeters. The radius is equivalent to half of the diameter, which implies r= 3 centimeters. Furthermore, we can see the height of the cylinder is 5 centimeters. Let's substitute these values into the formula to find the volume.

V_(Total)= π r^2 h

SubstituteII

r= 3, h= 5

V_(Total)= π * ( 3)^2 * ( 5)

CalcPow

Calculate power

V_(Total)= π * (9) * (5)

Multiply

Multiply

V_(Total)= 45 π cm^3

The volume of the total cylinder is 45 π cubic centimeters. Let's repeat this process to find the volume of the cylinder cut out. The diameter is labeled as 2 centimeters, which implies the radius is 1 centimeter. Furthermore, we can see the height of the cylinder is 5 centimeters. Let's substitute these values into the formula to find the volume.

V_(Cut out)= π r^2 h

SubstituteII

r= 1, h= 5

V_(Cut out)= π * ( 1)^2 * ( 5)

BaseOne

1^a=1

V_(Cut out)= π * (1) * (5)

Multiply

Multiply

V_(Cut out)= 5 π cm^3

The volume of the cylinder cut out is 5 π cubic centimeters. Finally, we will take the differences of the two volumes to find the volume of the remaining solid. V_(Remaining solid)= V_(Total)-V_(Cut out) ⇕ V_(Remaining solid)= 45 π-5 π = 40 π cm^3 The volume of the remaining solid is 40 π ≈ 125.7 cubic centimeters.