Sylvia conducts an experiment using two long pieces of a cord and a spherical ball that has been cut in half. The radius of the spherical ball is 8 centimeters. She wraps the first cord around the hemisphere of the ball until it is completely covered, as shown in Figure 1. She cuts the cord and removes it from the ball. She then wraps the second cord around the bottom circle of the ball until it is completely covered, as shown in Figure 2. She again cuts the cord and removes it from the circular base. Suppose the interior of one of the hemispheres was completely filled with glue. Some of this glue was used to cover the exterior of that hemisphere, not including its base, to a depth of approximately 0.5 centimeter so that the wrapped cord would stick. Given that the volume of glue used on the surface of the hemisphere is 64π cubic centimeters, what fraction of the original amount of glue that filled the hemisphere must be used to cover the exterior of the hemisphere as described? A - 3/8 B - 3/16 C - 3/32 D - 3/64
Sylvia conducts an experiment using two long pieces of a cord and a spherical ball that has been cut in half. The radius of the spherical ball is 8 centimeters. She wraps the first cord around the hemisphere of the ball until it is completely covered, as shown in Figure 1. She cuts the cord and removes it from the ball. She then wraps the second cord around the bottom circle of the ball until it is completely covered, as shown in Figure 2. She again cuts the cord and removes it from the circular base.
Suppose the interior of one of the hemispheres was completely filled with glue. Some of this glue was used to cover the exterior of that hemisphere, not including its base, to a depth of approximately 0.5 centimeter so that the wrapped cord would stick. Given that the volume of glue used on the surface of the hemisphere is 64π cubic centimeters, what fraction of the original amount of glue that filled the hemisphere must be used to cover the exterior of the hemisphere as described?
A - 3/8
B - 3/16
C - 3/32
D - 3/64
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