Geometric Modeling
Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A?
* 16 inches
Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters. What is the volume of the space filled with tissue paper in the packaging box?
* 198.264 cubic centimeters
An oblique cylinder has a radius of 10 units and slant length of 26 units. What is the volume of the cylinder?
* 2,400π cubic units
The radius of a sphere is 10 units. What is the approximate volume of the sphere? Use pi = 3.14 and round to the nearest whole cubic unit.
* 4187 cubic units
A silo is constructed using a cylinder with a hemisphere on top. The circumference of the hemisphere and the circumference of the cylinder are equal. The diameter of the circular base of the cylinder is 10 feet. The cylinder is 40 feet tall. One of the circular bases on the cylinder is in contact with the ground. What is the area of the surface of the silo that will be exposed to rain, wind, and sun?
* 450π square feet
A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile. How many deer live in the county? Round to the nearest whole number, if necessary.
* 5,852 deer
Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase. He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet.
* 8 ft3
A regular hexagon is shown (hypot = 10). What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.
* 9 in.
Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds?
* Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Select two options.
* The length of segment XY can be found by solving for a in 202 - 7.652 = a2. * The measure of the central angle, ∠ZXW, is 45°.
The more people living in an area, the more likely it is that public buses will be used. City A has a population of 51,242 and covers an area of 89.22 mi2. City B has a population of 50,178 and covers an area of 8.12 mi2. Which statement about use of public buses in the cities is most likely true?
* The residents of City B are more likely to use public buses because their city has a greater population density.
The table shows information about Town A in Illinois and Town B in Florida. If the two towns have the same population density, which must also be true?
* Town B has a population of approximately 5,138.
A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base. The cross section can be which of these shapes? Select three options.
* square * trapezoid * triangle
A solid right pyramid has a square base with an edge length of s units and a height of h units. Which expression represents the volume of the pyramid?
* v = 1/3 s2h units 3
An oblique square prism is shown. Which expression represents the volume of the prism?
* x2(x - 2) cubic units
