91Ó°ÊÓ

Does a right circular cylinder such as an aluminum can have a) symmetry with respect to at least one plane? b) symmetry with respect to at least one line? c) symmetry with respect to a point?

A polyhedron (not regular) has 14 vertices and 21 edges. How many faces must it have?

For the right triangular prism found in Exercise \(16,\) suppose that the sides of the triangular base measure \(3 \mathrm{ft}, 4 \mathrm{ft}\), and \(5 \mathrm{ft}\). The altitude is \(6 \mathrm{ft}\) in length. a) Find the lateral area of the prism. b) Find the total area of the prism. c) Find the volume of the prism.

In Exercises 15 to 20 , use the fact that \(r^{2}+h^{2}=\ell^{2}\) in \(a\) right circular cone (Theorem 9.3.6). Find the length of the radius \(r\) of a right circular cone in which \(h=6\) yd and \(\ell=8\) yd.

Find the total area (surface area) of a regular tetrahedron if each edge has a length of 6 in.

The total area (surface area) of a regular octahedron is \(32 \sqrt{3} \mathrm{ft}^{2} .\) Find the a) area of each face. b) length of each edge.

Find the volume and the surface area of a "closed box" that has dimensions of \(15 \mathrm{cm}, 20 \mathrm{cm},\) and \(0.25 \mathrm{m}\) (Hint: \(1 \mathrm{m}=100 \mathrm{cm} .)\)

A cereal box measures 2 in. by 8 in. by 10 in. What is the volume of the box? How many square inches of cardboard make up its surface? (Disregard any hidden flaps.)

Find the approximate volume of a sphere with radius length \(r=33.5 \mathrm{mm}\)

The measures of the sides of the square base of a box are twice the measure of the height of the box. If the volume of the box is 108 in \(^{3},\) find the dimensions of the box.