Question

the triangle shown is rotated about line m. what is the approximate base area of the resulting three - dimensional figure? area of a circle: $a = pi r^{2}$ 38 sq. cm 113 sq. cm 201 sq. cm 314 sq. cm

Explanation:

Step1: Identify the radius of the base circle

When the right triangle is rotated about line \( m \), the base of the resulting three - dimensional figure (a cone) is a circle. The radius of this circle is equal to the length of the leg of the right triangle that is perpendicular to line \( m \). From the diagram, the length of this leg is \( 6 \) cm. So, \( r = 6 \) cm.

Step2: Use the formula for the area of a circle

The formula for the area of a circle is \( A=\pi r^{2} \). Substitute \( r = 6 \) and \( \pi\approx3.14 \) into the formula.
\( A=\pi\times(6)^{2}= 3.14\times36=113.04\approx113 \) square centimeters.

Answer:

113 sq. cm