Constant volume tori The volume of a solid torus is given by V = ( π 2 / 4 ) ( R + r ) ( R − r ) 2 , where r and R are the inner and outer radii and R > r (see figure). a. If R and r increase at the same rate, does the volume of the torus increase, decrease, or remain constant? b. If R and r decrease at the same rate, does the volume of the torus increase, decrease, or remain constant?
Constant volume tori The volume of a solid torus is given by V = ( π 2 / 4 ) ( R + r ) ( R − r ) 2 , where r and R are the inner and outer radii and R > r (see figure). a. If R and r increase at the same rate, does the volume of the torus increase, decrease, or remain constant? b. If R and r decrease at the same rate, does the volume of the torus increase, decrease, or remain constant?
Solution Summary: The author explains that the volume of a torus with an inner radius r and an outer radius is, V=(pi 4)
Constant volume tori The volume of a solid torus is given by
V
=
(
π
2
/
4
)
(
R
+
r
)
(
R
−
r
)
2
, where r and R are the inner and outer radii and R > r (see figure).
a. If R and r increase at the same rate, does the volume of the torus increase, decrease, or remain constant?
b. If R and r decrease at the same rate, does the volume of the torus increase, decrease, or remain constant?
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