### Home > CALC > Chapter 1 > Lesson 1.2.3 > Problem1-54

1-54.

On graph paper, sketch the function $g ( x ) = \sqrt { 36 - x ^ { 2 } }$. Shade $A(g, 3 ≤ x ≤ 6)$, the region between $g(x)$ and the $x$-axis, for $3 ≤ x ≤ 6$. .

1. Use geometry to find this area. Hint: Draw in a radius to create two easier regions whose difference is the shaded region.

2. Find $A(g, 0 ≤ x ≤ 3)$.

3. Find $A(g, -3 ≤ x ≤ 6)$.

You should recognize $g$ as the equation of a semicircle, centered at the origin with radius $6$.
View the eTool. The height of the triangle is $5$ and the hypotenuse is $6$. Use these lengths to calculate the measure of the central angle.

Use the eTool below for parts (a) - (c).
Click the link at right for the full version of the eTool: Calc 1-54 HW eTool