The solid lies between planes perpendicular to the x-axis at&nbsp;x = -1 and x = 1. The cross-sections perpendicular to the&nbsp;x-axis between these planes are squares whose bases run from the&nbsp;semicircle y = - 21 - x2 to the semicircle y = 21 - x2.

Question

The solid lies between planes perpendicular to the x-axis at&amp;nbsp;x = -1 and x = 1. The cross-sections perpendicular to the&amp;nbsp;x-axis between these planes are squares whose bases run from the&amp;nbsp;semicircle y = - 21 - x2 to the semicircle y = 21 - x2.

Nick Camelot · Accepted Answer

The given information describes a solid that is bounded by two perpendicular planes, x=−1 and x=1, and the cross-sections perpendicular to the x-axis between these planes are squares. The bases of these squares are defined by the semicircles y=−21−x2 and y=21−x2.In order to visualize this solid, we can imagine slicing it perpendicular to the x-axis at various x-values between -1 and 1. At each x-value, the cross-section formed is a square. The length of each side of the square is determined by the difference between the y-values of the two semicircles at that x-value.To find the length of each side, we subtract the y-values of the semicircles at a given x-value:Side length = (21−x2)−(−21−x2)Simplifying the expression:Side length = 21−x2+21+x2Side length = 42Hence, the side length of each square cross-section is 42 units.To summarize, the solid is bounded by the planes x=−1 and x=1, and the cross-sections perpendicular to the x-axis between these planes are squares with a side length of 42 units.

The solid lies between planes perpendicular to the

Answered question

Answer & Explanation

New Questions in Math Word Problem