geometry b - unit 5: three-dimensional figures lessons 20-23
what is the approximate volume of the container?
55.22 cm^3
the following sphere has a radius of 3 inches. what is the correct formula to calculate the volume of this sphere?
v = 4/3π(3)^3
lesson 20
volumes
the following cylinder has a height of 7.2 and diameter of 6.8. what is the volume of the cylinder?
261.3 cm^3
wow many cubic inches of ice cream does it hold?
270
what is the volume of a tennis ball?
9.2 cm^3
lesson 23
density
zed is making a centerpiece for his dining room table by putting sand in a vase. he bought 25 kg of sand. assume the density of dry sand is 1,602 kg/m^3. what is the approximate volume of the sand in m^3?
0.015605
orion is constructing a rectangular box. the base of the box is a piece of wood with an area of 90 square inches. the volume of the box needs to have a volume of 1,080 cubic inches. what is the height of the box in inches?
12
wilma is building a box in the shape of a rectangular prism. the box needs to have a volume of 720 cubic inches and a height of 10 inches. which dimensions can she use for the base of the box? select all that apply.
12 in. by 6 in. 9 in. by 8 in.
jin's patio has an area of 200 square feet. she is covering the area with 3200 small rocks. what is the density of the rocks on the patio?
16
the following sphere has a diameter of 7 centimeters (cm). what is the volume of the sphere?
179.5 cm^3
what is the approximate volume of the space inside the container not filled by the tennis balls?
18.4 cm^3
the following cone has a slant height of 8.2 cm and a radius of 5.4 cm. what is the volume of the cone?
189.2 cm^3
the base of a rectangular pyramid is 7 cm long and 3 cm wide. if the pyramid has a height of 5 cm, what is its volume?
35 cubic cm
a portable cooler is 19 inches long, 14 inches wide, and 14 inches tall. what is the volume of the cooler in cubic inches?
3724
when inflated, a beach ball has a radius of 4.5 inches. approximately how many cubic inches of air does it hold?
382
what is the approximate height of the paper cones?
4
what is the minimum number of times she needs to fill (or partially fill) the bottle in order to reach her goal?
4
miriam is setting up a fishing game in a kiddie pool for her niece's birthday party. the pool has a circular base with a diameter of 4 feet and a height of 0.75 feet. she wants to fill the pool halfway so there is plenty of space left for the plastic fish. approximately how many cubic feet of water does she need?
4.7
a paint can is 10 cm tall and holds approximately 535 cubic centimeters of paint. what is the approximate area of the base of the can?
53.5 square centimeters
a moving box has a volume of 1.5 cubic feet and a mass of 9 pounds. what is the density of the contents of the box?
6
a neighborhood is home to 1550 residents. its area is 2.5 square miles. what is the population density in the neighborhood?
620
the following sphere has a radius of 18 millimeters (mm). what is the volume of the sphere?
7776π mm^3
use the figure to answer the question. https://cdstools.flipswitch.com/asset/media/1183315 which best describes the three-dimensional figure obtained from rotating the figure around the y-axis?
a cone with a radius of 1 unit
consider the following figure. https://h2.flipswitch.com/images/2019/Edited/cf3e3ef8-637a-491b-9f49-2a6f1ee6e3b9.png what solid of revolution is formed by rotating a right triangle about the vertical axis of rotation shown?
a cone with a radius of 12 units
which best describes the three-dimensional figure obtained from rotating the figure around the y-axis? a triangle
a cone with a radius of 3 units
which two-dimensional cross sections are squares? select all that apply.
a cross-section that is perpendicular to the base of a cube a cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same
kodi needs to refill the ink in his pen, so he needs to find its volume. which three-dimensional figure should he use to model the pen?
a cylinder
use the figure to answer the question. https://cdstools.flipswitch.com/asset/media/1183325 which best describes the three-dimensional figure obtained from rotating the figure around the y-axis?
a cylinder with a radius of 1 unit
which best describes the three-dimensional figure obtained from rotating the figure around the y-axis? a square
a cylinder with a radius of 2 units
the sports equipment pictured closely resembles which 3d shape?
a sphere
which of these real-life figures has a shape that most closely resembles a cone?
an erlenmeyer flask
which two-dimensional cross-sections are circles? select all that apply.
any cross-section of a sphere unless it touches the surface of the sphere a cross-section of a cylinder parallel to its base
what are the radius, height, and base area of the cylindrical container?
h = 10.4 cm r = 1.3 cm b = 5.31 cm^2
lesson 22
model with three dimensions
as the plane passes through the cylinder, what shape is created in the cross section?
rectangle
lesson 21
solids of revolution and cross sections
a cylindrical container holds four tennis balls, each with a diameter of 2.6 inches. the balls are stacked so they touch the container on the sides, top, and bottom. which solid figures can be used to model this situation?
sphere cylinder
in the formula for the volume of the cylinder, which quantity can be substituted for "lw"?
the area of circle, π ⋅ r^2
the right cone and right cylinder shown in the diagram have bases with the same area. the cone and cylinder also have the same height. which statement about the figures is true?
the cone can fill the cylinder exactly three times.
the following pyramid and prism have the same height and same base area. which statement about their volumes is true?
the volume of the pyramid is 1/3 the volume of the prism.
consider a triangular prism and a cylinder having the same base area and the same height. what can you say about their volumes?
the volumes are the same.
what two-dimensional cross sections could be created by slicing a triangular prism? select all that apply.
trapezoid rectangle triangle
which two-dimensional cross sections could be created by slicing a rectangular pyramid? select all that apply.
triangle trapezoid rectangle
