Pyramids Lesson 8-3
History When we think of pyramids we think of the Great Pyramids of Egypt. They are actually Square Pyramids, because their base is a Square.
Pyramids in Egypt The Great Pyramid of Khufu, at Giza, Egypt, is 751 feet long on each side at the base, is 450 feet high, and is composed of approximately 2 million blocks of stone, each weighing more than 2 tons. The maximum error between side lengths is less than 0.1%. The sloping angle of its sides is 51°51'. Each side is oriented with the compass points of north, south, east, and west. Each cross section of the pyramid (parallel to the base) is a square. Until the 19th century, the Great Pyramid at Giza was the tallest building in the world. At over 4500 years in age, it is the only one of the famous Seven Wonders of the Ancient World that remains standing. According to the Greek historian Herodotus, the Great Pyramid was built as a tomb for the Pharaoh Khufu.
A pyramid is typically described by the shape of its base A pyramid is typically described by the shape of its base. Parts of a Pyramid
Name that Pyramid 7 4 5 Hexagonal pyramid __________________ How many faces?_______ 7 Triangular pyramid Rectangular pyramid __________________ _______________________ How many faces?_______ How many faces?_______ 4 5
Parts of a Pyramid To find slant height, remember to use Pythagorean Theorem
Finding Slant Height Example
Volume of a pyramid A pyramid is a solid with a polygonal base and several triangular lateral faces.. The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. Square pyramid
Calculate the Volume of a Pyramid
Apply the volume formula! A regular pyramid is shown at the left. Find the volume of the pyramid to the nearest cubic unit. 267 cubic units
Triangular Pyramid The base is a triangle, so we need to use ½ bh! Base area= ½ (3)(5)=7.5
Apply the volume formula when you are not given the height What is the value of x? Half of the base length is 3 cm. Now, we can use the Pythagorean formula! We have a 3,4, 5 Pythagorean triple here! Now we can use the volume formula! V= 1/3 (6)(6)(4)=48 cm3
Cross Sections Suppose a plane intersects a square pyramid. Describe the different cross sections when a plane intersects a square pyramid. Cross sections Suppose a plane intersects a square pyramid. Describe the different cross sections when a plane intersects a square pyramid. A square smaller in area than the base. An isosceles triangle with its base Length the same as the length of the square. A single point
Summer is coming…. Skin cancer is the most common cancer in the United States. Current estimates are that one in five Americans will develop skin cancer in their lifetime. It is estimated that more than 8,500 people in the U.S. are diagnosed with skin cancer every day. It is estimated that 144,860 new cases of melanoma, 68,480 noninvasive (in situ) and 76,380 invasive, will be diagnosed in the U.S. in 2016. Noah goes to CVS to get some sunscreen for his day at the beach. He narrows it down to Bottle A and Bottle B. He thinks Bottle B is the better buy. Sean doesn’t agree. Which is the better buy? As Noah is about to make his purchase, Joaquin finds that Bottle C is on sale for $13.20. Joaquin tells Noah that he thinks Bottle C is the best buy. Is he right?
Sunscreen best buy solution
Smack down of the sunscreens: Bottle B VS. Bottle C Recall: Bottle B cost: $2.40/in3 Joaquin is a smart shopper!
Think about it… The winner is the square pyramid!! A prism made of oak wood has a density of 0.75 g/cm3 and dimensions of 4 cm by 5 cm by 10 cm. A regular square pyramid made of ash wood has a density of 0.526 g/cm3 with an altitude of 18 cm and the area of its base is 49 cm2. Which has a greater mass? Volume of prism= 200 cu.cm 0.75g/cm3 (200 cu.cm.)= 150 g Volume of pyramid= 294 cu.cm 0.526 g/cm3 (294cu.cm.)= 154.644 g The winner is the square pyramid!!
Practice Time!!! What shape is usually waiting for you at Starbucks? A line. Which triangles are the coldest? Ice-sosceles triangles