Question

the rectangle shown is rotated about line k. what is the approximate base area of the resulting figure? area of a circle: $a = pi r^2$ 31 sq. in. 50 sq. in. 79 sq. in. 314 sq. in.

Explanation:

Step1: Identify the radius

When the rectangle is rotated about line \( k \), the resulting figure is a cylinder. The base of the cylinder is a circle, and the radius \( r \) of this circle is the horizontal distance from line \( k \) to the side of the rectangle, which is 5 inches.

Step2: Calculate the area of the circle

Using the formula for the area of a circle \( A = \pi r^2 \), substitute \( r = 5 \) and \( \pi \approx 3.14 \).
\[
A = 3.14 \times 5^2
\]
\[
A = 3.14 \times 25
\]
\[
A = 78.5 \approx 79
\]

Answer:

79 sq. in.