Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height

t

as shown in the figure. Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius

d

through the center of a sphere of radius

D

and express the answer in terms of

t

.
$Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height t as shown in the figure. Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius d through the center of a sphere of radius D and express the answer in terms of t . A) V = \frac { 1 } { 6 } \pi t ^ { 2 } B) V = \frac { 1 } { 3 } \pi t ^ { 2 } C) V = \frac { 1 } { 6 } \pi t ^ { 3 } D) V = \frac { 1 } { 3 } \pi t ^ { 3 } E) V = \frac { 1 } { 4 } \pi t ^ { 3 }$

A)

V = \frac { 1 } { 6 } \pi t ^ { 2 }

V = \frac { 1 } { 3 } \pi t ^ { 2 }

V = \frac { 1 } { 6 } \pi t ^ { 3 }

V = \frac { 1 } { 3 } \pi t ^ { 3 }

V = \frac { 1 } { 4 } \pi t ^ { 3 }

Find the Area of the Region Bounded by the Parabola y=x2y = x ^ { 2 }y=x2

Multiple Choice

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Find the Area of the Region Bounded by the Parabola $y = x ^ { 2 }$

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