Thread: volume of shape by using perpendicular cross sections?

the base of a loudspeaker is determined by the two curves y= (x^2 / 10) and y= (-x^2 / 10) for 1< or= x< or= 4. for this loud speaker , the cross sections are perpendicular to the x-axis are squares. what is the volume of the loudspeaker in cubic units? i tried many different ways and keep getting 4.092 .. but the answer is supposed to be 8.184. which is what i get if i multiply it by two.. but why?? HELP.

Originally Posted by calcgeek_17

the base of a loudspeaker is determined by the two curves y= (x^2 / 10) and y= (-x^2 / 10) for 1< or= x< or= 4. for this loud speaker , the cross sections are perpendicular to the x-axis are squares. what is the volume of the loudspeaker in cubic units? i tried many different ways and keep getting 4.092 .. but the answer is supposed to be 8.184. which is what i get if i multiply it by two.. but why?? HELP.

We will do it using a little bit of hand-waving but it makes it easier. Break up this solid into many many pieces (cross-sections). Pick a cross section at a point . The width of this cross section is . While the base length is . We are told that the cross sections are squares which means that the volume of each cross section is . Now integrate that from .

Originally Posted by calcgeek_17

the base of a loudspeaker is determined by the two curves y= (x^2 / 10) and y= (-x^2 / 10) for 1< or= x< or= 4. for this loud speaker , the cross sections are perpendicular to the x-axis are squares. what is the volume of the loudspeaker in cubic units? i tried many different ways and keep getting 4.092 .. but the answer is supposed to be 8.184. which is what i get if i multiply it by two.. but why?? HELP.

side of a square cross-section is

dude. thats awesome! thank you! been working on this problem for weeks.. and i keep skipping it! my whole class has been struggling. not even my calc teacher knew. we were starting to say they had made a mistake on the practice AP exam.. =] thx!