Honors Geometry
Chapter 12 Supplement
Name: _____________________________________
1. Sears best interior paint, they say, covers 400 square feet per gallon. A windowless room with a wooden, unpainted floor is to be
painted (not the floor). Its’ dimensions are 25 feet by 20 feet by 8 feet. How many gallon containers should be purchased?
2. Find the space diagonal of a cube with total surface area 1296 cm2.
3. Two similar pyramids have base perimeters 12 and 48. How many times larger is the total surface area of the larger pyramid?
4. A cone is carved out of a hemisphere so that the vertex of the cone is at the bottom of the hemisphere. If the hemisphere has
diameter 18, find the total surface area of the solid.
5. Find the total surface area of a regular octahedron (8 faces, all are congruent equilateral triangles) if each edge has length 6.
6. Given a regular hexagonal pyramid with base perimeter 72 and altitude 8 3 , find the total surface area.
20
20
7. Find the total surface area and volume of the solid.
10
12
12
8. Find the total surface area and the volume of the truncated pyramid. The upper base and lower base are both squares. Each lateral
edge is 13. The upper and lower bases are parallel.
10
13
20
9. Find the total surface area and volume of a square pyramid with altitude 6 and base diagonal 16 2.
10. Find the volume of a cone with base diameter 10 and slant height 13.
11. Find the volume of the entire cone. Then find the volume of the piece that is not a
cone (The frustum)
3
10
10
12. An open topped rectangular box has a length of 10 cm, a height of 8 cm, and a width of 14 cm on the outside with a rectangular
prism cut from it uniformly 2 units from the outside and the bottom. Find the surface area of the solid.
13. A regular square pyramid has height 12 and slant height 13. Find the lateral surface area and the total surface area of the pyramid.
14. A cone has diameter 12 ft. and height 9 ft. A cylinder is placed inside the cone so the base of the cylinder is concentric with the
base of the cone and the upper base of the cylinder is contained in the surface of the cone. If the volume of the cone is nine times the
volume of the cylinder, find the dimensions of the cylinder.
15. A tennis ball can is a cylinder with three spherical balls tangent to each other and the sides of the can. A tennis ball has a surface
area of 6.25. Find the volume between the balls and the can.
16. A sphere with diameter 12 mm rests inside a cone tangent to the sides and to the top. The cone has diameter 12 3 . Find the
volume inside the cone but outside the sphere.
17. Find the surface area and volume of the following figures. Round your answers to the nearest hundredth. Use millimeters as your
units.
a)
12
10
b)
18. Find the amount of glass needed to cover the sides of the greenhouse shown. The bottom, front, and back are not glass.
19. Given: Regular square pyramid PABCD.
Altitude PQ has a length of 15 cm.
DB = 16 2 cm
a) Find the length of QS.
b) Find the length of AD.
c) Find the area of the base of the pyramid.
d) Find the lateral area of the pyramid.
e) To the nearest tenth, find PC.
f) Find the surface area of the pyramid.
g) Find the volume of the pyramid.
20. Find the total surface area of the figure to the right.
21. Find the total surface area and volume of the figure to the right.
22. Find the total surface area and volume of the figure to the right.
23. Find the total surface area and volume of the figure to the right.
24. Find the total surface area and volume of the figure to the right.
25. The figure below has a total height of 24 m and a base which is a square with side length 5 m, find the total surface area and
volume.
26. A plastic bowl is in the shape of a cylinder with a hemisphere cut out. What is volume of plastic used to make the bowl?
27. Find the total surface area and volume of the figure to the right.
28. Find the total surface area of the figure to the right.
29. A right prism has a rectangular base with the length of one side 4 feet. The right prism also has a surface area of 480 ft2 and a
width of 16 feet. Find the height of the figure.