lionsshare wrote:

A circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band?

(1) x = 0.5
(2) The height of the tub is 1 meter.

We are given a cylinder with a shaded band painted around its circumference. We know that the height of the band is x meters, and we also know that the shape of the band is a hollow cylinder (i.e., a cylinder without the top and bottom circular bases). We need to determine the surface area of the band. We know the surface area of a cylinder (when it has the top and bottom circular bases) is:

surface area = 2Ï€r^2 + 2Ï€rh

Notice that the 2Ï€r^2 is the area of the two circular bases of the cylinder (had it been a solid one). However, here the cylindrical band is hollow, thus its surface area is:

surface area = 2Ï€rh

We can replace h with x since that is the height of the band, so we have:

surface area of band = 2Ï€rx

So if we can determine the value of r and x, we can determine the surface area of the band.

Statement One Alone:

x = 0.5

While we have the value of x, without knowing the value of r, we cannot determine the surface area of the band. Statement one is not sufficient to answer the question.

Statement Two Alone:

The height of the tub is 1 meter.

Knowing the height of the tub does not provide us with the value of x or r. Statement two is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two together we still do not have a value for r and thus we cannot determine the surface area of the band.

Answer: E