5 Use derivatives to find approximate changes in geometric

Last updated: 4/13/2023

5 Use derivatives to find approximate changes in geometric measurements For all the formulas below be able to find the differential of one variable with respect to another variable and find the rate of changes at given specified values Perimeter and Area of Plane Figures Triangle P a b c A Rectangle P 21 2 Parallelogram P 2a 26 A bk Trapezoid Pwa b c d Circle C 2tr A ar Volume and Surface Area of Solid Figures Rectangular Prism V Ink S 2w 2h 2wh Right Circular Cylinder Vwr h S 2x 2xrk Sphere Smlar Right Circular Cone Swar ars For the circle and sphere 1 a Find dC in term of dr What is dC if dr 1cm b Express the radius r in terms of the circumference C Find dr in terms of dC Find dr if dC 2 cm Ans a dC 2ndr dC 2 cm if dr 1 cm b r C 2n dr dC 2n dr 1 cm 2 a Find dA in term of dr What is dA if when r 12 cm and dr 0 1 cm b Express the radius r in terms of the area A Find dr in terms of dA Find dr if A 16 cm and that dA 1 cm 3 a Find area A in terms of the circumference C Find dA in term of dC What is dA if when C 87 cm and dC 0 1 cm b Find the circumference C in terms of the area A Find dC in terms of dA Find dC if A 167 cm and that dA 1 cm Ans a A C 4x dA C 2n dC dA 0 4 cm b C 2n A 2 dC 2A 2dA dC 4 cm 1 a Find dV in term of dr What is dV if dr 0 1 cm when r 10 cm b Express the radius r in terms of the volume V Find dr in terms of dV Find dr if dV 1 cm when V 36 cm Ans b r v dr 2 vdv dr 36 0 190 2 dV 2 a Find dS in term of dr What is dS if dr 0 1cm when r 10 cm b Express the radius r in terms of the surface area S Find dr in terms of dS