Exercise 6 Page 594

We are asked to match each cylinder with its approximate volume.

The volume of a cylinder if given by the following formula. Here r is the radius of the circular base, and h is the height of the cylinder.

Let's then evaluate the volumes one by one, starting with the first cylinder.

First Cylinder

Here is what we know about the first cylinder. radius &= 4.1 ft, height &= 5 ft Notice that we have everything to find its volume — the radius and the height. Let's then substitute 4.1 ft for r and 5 ft for h in the formula. Then we will evaluate the expression. Note that we will use 3.14 for π.

The volume of the cylinder is about 264 ft^3.

Second Cylinder

Here is what we know about the second cylinder. diameter &= 8 ft, height &= 2.2 ft See that we are given the diameter, not the radius of the base. Since the diameter is twice the radius, we can divide the given value by 2. This will give us the radius. radius &= 8 ft2 or4 ft, height &= 2.2 ft Now we have everything to find its volume. Let's then substitute 4 ft for r and 2.2 ft for h in the formula. Then we will evaluate the expression.

The volume of the cylinder is about 111 ft^3.

Third Cylinder

Here is what we know about the last cylinder. diameter &= 6.2 ft, height &= 3 ft Once again, we are given the diameter, not the radius of the base. Let's then divide the given diameter by 2. This will give us the radius. radius &= 6.2 ft2 or3.1 ft, height &= 3 ft Now we have everything to find its volume. Let's then substitute 3.1 ft for r and 3 ft for h in the formula.

The volume of the cylinder is about 91 ft^3.

Cylinders and Areas

We can now match each cylinder with its approximate value.