Volume and surface of solids

1103235601

Level: 
C
Find the volume of a right pyramid whose base is a regular hexagon each side of which is \( 6\,\mathrm{cm} \) and height \( 8\,\mathrm{cm} \) (see the picture).
\( 144\sqrt3\,\mathrm{cm}^3 \)
\( 72\sqrt3\,\mathrm{cm}^3 \)
\( 48\sqrt3\,\mathrm{cm}^3 \)
\( 24\sqrt3\,\mathrm{cm}^3 \)

1103235602

Level: 
C
Find the surface area of a right pyramid whose base is a regular hexagon each side of which is \( 6\,\mathrm{cm} \) and height \( 9\,\mathrm{cm} \) (see the picture).
\( 162\sqrt3\,\mathrm{cm}^2 \)
\( 15\sqrt3\,\mathrm{cm}^2 \)
\( 9\left(\sqrt3+6\sqrt{13}\right)\,\mathrm{cm}^2 \)
\( 117\sqrt3\,\mathrm{cm}^2 \)

1103235603

Level: 
C
The base of a right pyramid is a regular hexagon of side \( 4\,\mathrm{m} \) and its slant surfaces are inclined to the horizontal at an angle of \( 30^{\circ} \) (see the picture). Find the volume.
\( 16\sqrt3\,\mathrm{m}^3 \)
\( 72\sqrt3\,\mathrm{m}^3 \)
\( 48\sqrt3\,\mathrm{m}^3 \)
\( 24\sqrt3\,\mathrm{m}^3 \)

1103235604

Level: 
C
The area of the base of a regular hexagonal pyramid is \( 54\sqrt3\,\mathrm{cm}^2 \) and the lateral edge is two times the length of the base edge (see the picture). Find the volume of the pyramid.
\( 324\,\mathrm{cm}^3 \)
\( 108\sqrt3\,\mathrm{cm}^3 \)
\( 972\,\mathrm{cm}^3 \)
\( 216\,\mathrm{cm}^3 \)

1103235605

Level: 
C
A regular hexagonal pyramid has the perimeter of its base \( 12\sqrt3\,\mathrm{cm} \) and its slant height is \( 5\,\mathrm{cm} \). Find the surface area.
\( 48\sqrt3\,\mathrm{cm}^2 \)
\( 72\sqrt3\,\mathrm{cm}^2 \)
\( 30\sqrt3\,\mathrm{cm}^2 \)
\( 96\sqrt3\,\mathrm{cm}^2 \)

1103235606

Level: 
C
Find the volume of a regular hexagonal prism with lateral edge length of \( 12\,\mathrm{cm} \) and a base edge length of \( 9\,\mathrm{cm} \) (see the picture).
\( 1458\sqrt3\,\mathrm{cm}^3 \)
\( 243\sqrt3\,\mathrm{cm}^3 \)
\( 1944\sqrt3\,\mathrm{cm}^3 \)
\( 729\sqrt3\,\mathrm{cm}^3 \)

1103235607

Level: 
C
Find the surface area of a regular hexagonal prism with lateral edge length of \( 10\sqrt3\,\mathrm{cm} \) and a base edge length of \( 6\,\mathrm{cm} \) (see the picture).
\( 468\sqrt3\,\mathrm{cm}^2 \)
\( 414\sqrt3\,\mathrm{cm}^2 \)
\( 168\sqrt3\,\mathrm{cm}^2 \)
\( 408\sqrt3\,\mathrm{cm}^2 \)

9000120308

Level: 
C
The height \(v\) of a regular hexagonal prism is a double of its side \(a\). The volume of the prism is \(648\sqrt{3}\, \mathrm{cm}^{3}\). Use this information to find the length of the longest solid diagonal in the prism.
\(12\sqrt{2}\, \mathrm{cm}\)
\(10\sqrt{6}\, \mathrm{cm}\)
\(12\sqrt{6}\, \mathrm{cm}\)
\(6\sqrt{10}\, \mathrm{cm}\)
\(\sqrt{432}\, \mathrm{cm}\)