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Chapter 6 | Applications of Integration
103. Yogurt containers can be shaped like frustums. Rotate the line y = 1 m x around the y -axis to find the volume between y = a and y = b .
106. A better approximation of the volume of a football is given by the solid that comes from rotating y = sin x around the x -axis from x =0 to x = π . What is the volume of this football approximation, as seen here?
107. What is the volume of the Bundt cake that comes from rotating y = sin x around the y -axis from x =0 to x = π ?
104. Rotate the ellipse ⎛ ⎞ ⎠ =1 around the x -axis to approximate the volume of a football, as seen here. ⎝ x 2 / a 2 ⎞ ⎠ + ⎛ ⎝ y 2 / b 2
105. Rotate the ellipse ⎛
⎞ ⎠ +
⎛ ⎝ y 2 / b 2
⎞ ⎠ =1 around the
⎝ x 2 / a 2
y -axis to approximate the volume of a football.
For the following exercises, find the volume of the solid described.
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