3-D shapes (Cross sections of prisms and cylinders)：練習問題

A cylinder stands upright on its circular base. If we cut it with a horizontal plane that is parallel to the base, what is the shape of the cross section?

A solid cylinder with a base radius of \(4\text{ cm}\) and height of \(10\text{ cm}\) is cut horizontally by a plane parallel to its base. What is the diameter of the resulting cross section?

A solid cylinder with height \(12\text{ cm}\) and base diameter \(6\text{ cm}\) is sliced parallel to its base into \(3\) identical smaller cylinders. By how much does the total surface area increase compared to the original cylinder?

A prism stands upright on its base. If we cut the prism with a plane that is parallel to its base, what can be said about the resulting cross section?

A solid cylinder with radius \(5\text{ cm}\) and height \(14\text{ cm}\) is cut completely along a plane parallel to its axis into two identical halves. What is the area of the flat rectangular cross section exposed along the cut?

If a cylinder is cut by a plane parallel to its circular base, what is the shape of the resulting cross section?

A solid right cylinder with base diameter \(12\text{ cm}\) is cut by a horizontal plane parallel to its circular base. Find the circumference of the boundary of the cross section in terms of \(\pi\).

A nonagonal prism (base with 9 sides) is sliced by three different planes all parallel to its base, dividing the prism into four smaller prisms. Find the total sum of the number of vertices and the total sum of the number of edges across all four resulting smaller prisms.

A solid shape is a prism whose base is an equilateral triangle with a side length of \(8\text{ cm}\) and height \(15\text{ cm}\). The prism is cut horizontally by a plane parallel to its base to form two smaller pieces.

a) What 2-D shape is the cross section formed by this cut?
b) What is the perimeter of this cross section in \(\text{cm}\)?
c) How many vertices do the two resulting pieces have in total?

Consider a solid cylinder and a solid right pentagonal prism.

a) A plane cuts through the cylinder completely parallel to its circular base. Describe the geometric shape of the resulting cross section.

b) If the diameter of the circular base of the cylinder is \(14\text{ cm}\), find the area of this cross section. (Take \(\pi = \frac{22}{7}\))

c) The cylinder and the pentagonal prism each have one cut parallel to their respective bases. Let the number of vertices on the cylinder's cross section be \(V_1\), and the number of vertices on the pentagonal prism's cross section be \(V_2\). Find the value of \(V_1 + V_2\).