### Volume of a Solid with Square Cross-Sections**Description:**The base of a certain solid is the area bounded above by the graph of $ y = f(x) = 9 $ and below by the graph of $ y = g(x) = 4x^2 $. Cross-sections perpendicular to the $ x $-axis are squares.**Graph Explanation:**- **Base View:** The graph shows two functions: - $ y = 9 $ (horizontal line), indicating the constant upper boundary. - $ y = 4x^2 $ (parabola), representing the lower boundary.- **Cross-Section:** A vertical line segment is shown perpendicular to the $ x $-axis, demonstrating the square cross-section.**Formula for the Volume:**To find the volume of the solid, we use the formula:\[V = \int_a^b A(x) \, dx\]**Steps to Calculate the Volume:**1. **Lower Limit of Integration** ($ a $): *Enter value here*2. **Upper Limit of Integration** ($ b $): *Enter value here*3. **Side of Square Cross-Section** ($ s $): The side $ s $ of the square cross-section is the following function of $ x $: *Enter formula here*4. **Area of Cross-Section** ($ A(x) $): \[ A(x) = \text{{side}}^2 \quad \text{(since it's a square)} \]5. **Volume of the Solid** ($ V $): \[ V = \int_a^b A(x) \, dx \] *Enter calculated value here*This setup allows you to understand the bounds and calculate the volume using integration with respect to $ x $.

Answered: Image /qna-images/answer/1b7b66dd-b64e-4e47-a014-9e0d2059aec8.jpg Formula for volume V=∫abAxdx The volume bounded by the curves y=fx=9 and y=gx=4x2 For getting intersection points we have fx=gx ⇒ 9=4x2 ⇒ x2=94 ⇒ x = 94 ⇒ x=±32 =±1.5 Thus the lower limit of the integration is a = - 1.5 the upper limit of the integration is b = 1.5 The square cross section defined by fx-gx Ax=fx-gx=9-4x2 Using the above information the required volume is given by V=∫-1.51.59-4x2dx ⇒ V=9x-4x33-1.51.5 ⇒ V=91.5-431.53-9-1.5-43-1.53 ⇒ v=291.5-431.53 ⇒ v=18 Thus the volume of the solid is V = 18 cubic units Answers: The lower limit of the integration is a = - 1.5 The upper limit of the integration is b = 1.5 The square cross section defined by fx-gx Thus the volume of the solid is V = 18 cubic units