For each pair of solids, determine if their volumes are the same or different. If the volumes are different, identify the solid with the greatest volume. Explain your reasoning. 1. A prism and a pyramid with the same height, but the pyramid's base has 3 times the area of the prism's base. The prism's volume is [ Select ] the pyramid's volume. 2. A pyramid and cylinder have bases with the same area, but the cylinder's height is 3 times the height of the pyramid. The pyramid's volume is [ Select ] v the cylinder's volume. 3. A cone and cylinder have the same height, but the cone's radius is 3 times the length of the cylinder's radius. The cone's volume is ( Select] the cylinder's volume.
For each pair of solids, determine if their volumes are the same or different. If the volumes are different, identify the solid with the greatest volume. Explain your reasoning. 1. A prism and a pyramid with the same height, but the pyramid's base has 3 times the area of the prism's base. The prism's volume is [ Select ] the pyramid's volume. 2. A pyramid and cylinder have bases with the same area, but the cylinder's height is 3 times the height of the pyramid. The pyramid's volume is [ Select ] v the cylinder's volume. 3. A cone and cylinder have the same height, but the cone's radius is 3 times the length of the cylinder's radius. The cone's volume is ( Select] the cylinder's volume.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
![For each pair of solids, determine if their volumes are the same or different. If the
volumes are different, identify the solid with the greatest volume. Explain your
reasoning.
1. A prism and a pyramid with the same height, but the pyramid's base has 3 times
the area of the prism's base. The prism's volume is [ Select ]
the
pyramid's volume.
2. A pyramid and cylinder have bases with the same area, but the cylinder's height
is 3 times the height of the pyramid. The pyramid's volume is
[ Select ]
v the cylinder's volume.
3. A cone and cylinder have the same height, but the cone's radius is 3 times the
length of the cylinder's radius. The cone's volume is [ Select]
the
cylinder's volume.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7821cc1-4779-4de5-b265-25dfd86c2727%2Fb0608c6f-8140-4d74-8b6a-ebf40e8f533d%2Fvpvg4hq_processed.png&w=3840&q=75)
Transcribed Image Text:For each pair of solids, determine if their volumes are the same or different. If the
volumes are different, identify the solid with the greatest volume. Explain your
reasoning.
1. A prism and a pyramid with the same height, but the pyramid's base has 3 times
the area of the prism's base. The prism's volume is [ Select ]
the
pyramid's volume.
2. A pyramid and cylinder have bases with the same area, but the cylinder's height
is 3 times the height of the pyramid. The pyramid's volume is
[ Select ]
v the cylinder's volume.
3. A cone and cylinder have the same height, but the cone's radius is 3 times the
length of the cylinder's radius. The cone's volume is [ Select]
the
cylinder's volume.
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