2) What is the volume of a fidget spinner when it is spun?
3) Given the rectangle revolving about the \(y\)-axis:
Note, this site might be helpful for solids of revolution problems. a) What is the area of the rectangle? b) What is the shape of the solid when the rectangle is revolved? c) What is the total surface area of the solid? d) What is the volume of the solid? |
12) Describe the solid formed when the triangle pictured is revolved about the line \(y = -x + 3\).
13) What are the shapes of the cross sections of these rectangular prisms?
14) What are the shapes of the cross sections of these cones (sometimes called “conic sections”)?
15) What is the shape and area of the cross section perpendicular to the base of the right cylinder with a radius of \(4.5\)?
16) What is the shape and area of the cross section perpendicular to the base of the right cone with a diameter of \(4\)?
17) What is the shape and area of the cross section parallel to the base of the right cone?
18) Below is a sphere with two cross sections, one of which passing through the center of the sphere at point \(P\).
a) Name the “Great Circle.”
b) What are the shapes of the cross sections?
c) If \(\overline {PQ}\) has a length of \(4\) and the radius of the sphere (\(\overline{PB}\)) has a length of \(5\), then what is the length of \(\overline{QD}\)?
d) What is the area of the cross section passing through point \(Q\)?
a) Name the “Great Circle.”
b) What are the shapes of the cross sections?
c) If \(\overline {PQ}\) has a length of \(4\) and the radius of the sphere (\(\overline{PB}\)) has a length of \(5\), then what is the length of \(\overline{QD}\)?
d) What is the area of the cross section passing through point \(Q\)?
19) Figure 1 is a regular hexagonal prism with a height of \(9\) and a horizontal cross section hexagon (section A) with a side length of \(4\). Figure 2 is a cylinder with a height of \(9\) and a horizontal cross section (section B). If cross section region A is equal in area to cross section region B, then what is the volume of Figure 2? Round answer to the nearest tenth.