To find the area of the face of the clock described by the minute hand in 35 minutes, we need to find the length of the arc covered by the minute hand and then use it to calculate the area.

Length of Arc Covered by the Minute Hand:
The minute hand of the clock is 12 cm long. In 60 minutes, it covers a complete circle, which is equivalent to the circumference of the clock face. The formula for the circumference of a circle is given by:

C = 2πr

where C is the circumference and r is the radius.

In this case, the radius is equal to the length of the minute hand, which is 12 cm. So, the circumference of the clock face is:

C = 2π(12) = 24π cm

In 60 minutes, the minute hand covers the entire circumference. Therefore, in 35 minutes, it covers:

35/60 * 24π = 7/12 * 24π = 14π cm

Area of the Face of the Clock:
To find the area of the face of the clock described by the minute hand in 35 minutes, we need to calculate the area of the sector formed by the minute hand.

The formula for the area of a sector of a circle is given by:

A = (θ/360) * πr^2

where A is the area, θ is the central angle in degrees, and r is the radius.

In this case, the central angle is 35/60 * 360 = 210 degrees (since the minute hand covers 35 minutes out of 60 minutes, and each minute corresponds to 6 degrees on the clock face).

Substituting the values into the formula, we get:

A = (210/360) * π(12)^2
= (7/12) * π(144)
= 7π * 12
= 84π cm^2

Approximating π to 3.14, we have:

Area = 84 * 3.14
≈ 264 cm^2

Therefore, the area of the face of the clock described by the minute hand in 35 minutes is approximately 264 cm^2.

Hence, option B is the correct answer.