- Explaining Volume Formulas - Using Volume Formulas - Cross Sections of Three Dimensional Objects
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Created by Elexali Olayvar
over 3 years ago
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Close
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Created by Elexali Olayvar
over 3 years ago
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A cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. How much gas can the pressure vessel hold when full?
A.
54π cubic feet
B.
81π cubic feet
C.
108π cubic feet
D.
324π cubic feet
A funnel is made up of a partial cone and a cylinder as shown in the figure. The maximum amount of liquid that can be in the funnel at any given time is 16.59375π cubic centimeters. Given this information, what is the volume of the partial cone that makes up the top part of the funnel?
A.
15.75π cm^3
B.
17.25π cm^3
C.
16.33π cm^3
D.
12.5π cm^3
A liquid-filled glass pyramid is being erected as part of a museum attraction. The pyramid is designed to be 15 feet tall with a rectangular base that is 10 feet long and 6 feet wide. What is the total amount of liquid that the pyramid can hold?
A.
156 cubic feet
B.
278 cubic feet
C.
300 cubic feet
D.
324 cubic feet
A conical paper cup has dimensions as shown in the diagram. How much water can the cup hold when full?
A.
30π cm^3
B.
35π cm^3
C.
40π cm^3
D.
45π cm^3
A machine part consists of a half sphere and a cylinder, as shown in the figure. The total volume of the part is ____
π cubic inches.
The image shows a reconstruction of a pyramid with a square base. What is the best estimate for the volume of the pyramid?
A.
1,460,040 m^3
B.
2,433,400 m^3
C.
4,380,120 m^3
D.
7,300,200 m^3
A conical container can hold 120π cubic centimeters of water. The diameter of the base of the container is 12 centimeters.
The height of the container is ____
centimeters. If its diameter and height were both doubled, the container's capacity would be
____ times its original capacity.
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of `pi`.)
A.
452.16 cm^3
B.
840.54 cm^3
C.
1,055.04 cm^3
D.
1,456.96 cm^3
The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?
A.
800 cubic feet
B.
1,000 cubic feet
C.
1,200 cubic feet
D.
2,000 cubic feet
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.
The volume of pyramid A is _____
the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ____
the volume of pyramid A.
The volume of the pyramid shown in the figure is ___
cubic centimeters. If the slant height of the pyramid increases by 4 centimeters and its height increases by 2 centimeters, the volume of the pyramid increases by
___ cubic centimeters.
A prism whose base is a 9-sided polygon is intersected by a plane. In which case could the cross section be a 10-sided polygon?
A.
when the plane is parallel to the base of the prism
B.
when the plane is perpendicular to the base and contains two edges of the prism
C.
when the plane is perpendicular to the base and contains one edge of the prism
D.
when the plane makes a narrow angle with the base
A triangular pyramid is cut by a plane. In which case is the cross section a quadrilateral?
A.
when the plane is perpendicular to the base and passes through the apex
B.
when the plane is parallel to the base of the pyramid
C.
when the plane intersects the base and two lateral faces of the pyramid
D.
when the plane intersects the base and all three lateral faces of the pyramid
One of the corners of a cube is sliced off. The resulting cross section will have a minimum of ___
sides.
The diagram shows a cone and its axis of rotation. Which type of cross section is formed when the cone is intersected by a plane containing the axis of rotation?
A.
a circle
B.
an isosceles triangle
C.
a parabola
D.
an oval
A cylinder is sliced by a plane that is not parallel to the base and intersects only the lateral surface. The resulting cross section is
_____.
