Question
Find the volumes of the solids in Exercises $1-10$ .The base of a solid is the region bounded by the graphs of $y=\sqrt{x}$ and $y=x / 2 .$ The cross-sections perpendicular to the $x$ -axis area. isosceles triangles of height 6.b. semi-circles with diameters running across the base of the solid.
Step 1
Setting these two equal to each other, we get $\sqrt{x}=x/2$. Squaring both sides, we get $x=x^2/4$. Solving for $x$, we get $x=0$ and $x=4$. So, the region bounded by the two curves is from $x=0$ to $x=4$. Show more…
Show all steps
Your feedback will help us improve your experience
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the volumes of the solids in Exercises $1-10$. The base of a solid is the region between the curve $y=2 \sqrt{\sin x}$ and the interval $[0, \pi]$ on the $x$ -axis. The cross-sections perpendicular to the $x$ -axis are a. equilateral triangles with bases running from the $x$ -axis to the curve as shown in the accompanying figure. b. squares with bases running from the $x$ -axis to the curve.
Applications of Definite Integrals
Volumes Using Cross-Sections
Find the volumes of the solids in Exercises $1-10$ . The base of a solid is the region bounded by the graphs of $y=3 x, y=6,$ and $x=0 .$ The cross-scctions perpendicular to the $x$ -axis are a. rectangles of height 10 . b. rectangles of perimeter 20 .
Find the volumes of the solids in Exercises $1-10$ . The solid lies between planes perpendicular to the $y$ -axis at $y=0$ and $y=2 .$ The cross-sections perpendicular to the $y$ -axis are circular disks with diameters running from the $y$ -axis to the parabola $x=\sqrt{5} y^{2}$
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD