91Ó°ÊÓ

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.

Consider any regular pyramid. Indicate which line segment has the greater length: a) Slant height or altitude? b) Lateral edge or radius of the base?

Consider any regular pyramid. Indicate which line segment has the greater length: a) Slant height or apothem of base? b) Lateral edge or slant height?

Find the total area (surface area) of a regular hexahedron if each edge has a length of \(4.2 \mathrm{cm}\)

Use the fact that \(r^{2}+h^{2}=\ell^{2}\) in a right circular cone (Theorem 9.3.6). Find the length of the slant height \(\ell\) of a right circular cone with \(r=6\) in., length of altitude \(h,\) and \(\ell=2 h\) in.

Given that \(100 \mathrm{cm}=1 \mathrm{m},\) find the number of cubic centimeters in 1 cubic meter.

Use Theorem 9.2 .1 in which the lengths of apothem a, altitude \(h,\) and slant height \(\ell\) of a regular pyramid are related by the equation \(\ell^{2}=a^{2}+h^{2}\). In a regular square pyramid whose base edges measure 8 in., the apothem of the base measures 4 in. If the altitude of the pyramid is 8 in., find the length of its slant height.

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 with \(\ell=12\) in, and \(h=3 r\) in.

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

Use Theorem 9.2 .1 in which the lengths of apothem a, altitude \(h,\) and slant height \(\ell\) of a regular pyramid are related by the equation \(\ell^{2}=a^{2}+h^{2}\). In a regular hexagonal pyramid whose base edges measure \(2 \sqrt{3}\) in., the apothem of the base measures 3 in. If the slant height of the pyramid is 5 in., find the length of its altitude.