222 Part 3: The Shape of the World
The area of its base is B =^12 ap =^12 (2)(18) = 18 square inches. For this pyramid, the height is about
7.75 inches. Plug those numbers into the formula.VBh
1
31
3
18 7.75 46.5The volume is about 46.5 cubic inches. Now consider a square pyramid with an edge 12 feet
long and a height of 18 feet. If you plug those numbers into the formula, you get V =^13 Bh =
1
312 18 1
3(^2) 144 18 864. The pyramid will have a volume of 864 cubic feet.
MATH IN THE PAST
The Great Pyramid of Giza, the largest of the three famous structures, is a square
pyramid with a base 756 feet on each side and a height of 455 feet. That gives it a
volume of over 86 million cubic feet. However, there isn’t actually that much room
inside it, because much of the space is occupied by the stones from which it was built.
CHECK POINT
Find the volume of each pyramid. V =^13 Bh
- A square pyramid with a slant height of 13 inches and a side of 10 inches.
- A square pyramid 4 inches on each side with a slant height of 5 inches.
- A triangular pyramid with a slant of 10 cm, whose base is an equilateral triangle 12 cm on a
side, with an area of 62.4 square centimeters. - A pyramid with a slant height of 18 cm and regular pentagon as a base. The regular penta-
gon has a perimeter of 50 cm and an area of 172 square centimeters. - A hexagonal pyramid with a slant height of 10 inches. The regular hexagon that forms the
base has a perimeter of 60 inches and an area of 260 square inches.
Cylinders
Prisms and pyramids are solids formed from polygons, but there are also solids whose bases are
circles. The good news is that they have a lot in common with prisms and pyramids.
A solid with two parallel bases that are circles (instead of polygons) is called a cylinder and has a
lot in common with prisms.