Very important! answer fully jeremy and arnold were thinking about their recent math lessons on the volume of a cylinder and the volume of a cone. they were curious to see how many cones it would take to fill a cylinder. “let’s just make the shapes and see for ourselves,” suggested jeremy. while arnold thought it was a good idea, he and jeremy struggled to construct the shapes so that the radius and heights of each figure were the same. will you them in their investigation? (if you don’t want to use the shapes they provided, you can use any can or cone but they have to be the same height and have the same diameter) part i: construction nets for a cone and a cylinder are provided. cut out each shape and secure the edges with a piece of tape. part ii: filling the shapes fill the cone with a dry ingredient like rice or beans. pour the contents of the cone into the cylinder. repeat this process until the cylinder is full. how many cones does it take to fill the cylinder? write the formulas for the volume of each shape. vcyl = vcone = explain the relationship between the volume of the cylinder and the volume of the cone.

Find the magnitude of the torque about p if an f = 80-lb force is applied as shown. (round your answer to the nearest whole number.) ft-lb

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. increase the area of the base of the square pyramid by a factor of ten. increase the height of the cylinder by a factor of ten. increase the radius of the cone by a factor of ten. increase the radius of a sphere by a factor of ten. juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a cube with a side length of 12 feet a cone with a diameter of 12 feet and a height of 10 feet a square pyramid with a base side length of 12 feet and a height of 9 feet a hemisphere with a diameter of 12 feet marion has a bicycle that she is planning to take for a ride. the rim of the rear wheel lies 41 cm from the center of the wheel. the tire itself has a thickness of 3 cm.in order to marion to ride her bicycle 96,712 cm, approximately how many rotations will the rear wheel make? 350 15.9 376 5133 an isosceles trapezoid has perimeter of 42 inches. each of the congruent nonparallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? 10 inches and 16 inches 12 inches and 20 inches 16 inches and 16 inches 10 inches and 22 inches

Which statement accurately explains whether a reflection over the y-axis and a 270° counterclockwise rotation would map figure acb onto itself? a coordinate plane with figure acb with point a at 1, 1, c at 3, 4 and b at 5, 1 yes, a″c″b″ is located at a″(1, 1), c″(4, 3), and b″(1, 5) yes, a″c″b′ is located at a″(1, 1), c″(3, 4), and b″(5, 1) no, a″c″b″ is located at a″(1, 1), c″(4, 3), and b″(1, 5) no, a″c″b″ is located at a″(1, 1), c″(3, 4), and b″(5, 1)