An inverted pyramid is being filled with water at a censta nt rate of 3D cubic centimeters per seccrnd. The pyramid, at the top, has the shape of a square with sides crf length 6 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 5 cm. cmi'sec h solution : 6 cm 6cm 8 cm h We have square pyramid with base bom and height 8 cm . Let Water be filled inside this pyramid with base xem and height h'em.Water is filled at a constant rate of 30 cms / Secr i.e dv - 30 em' / sec We have to find Rate of Water level rising when water level is 5 cm i.e We have to find oh when h= 5 cm Now Volume of Water filled V 2 6From above diagram, x 2 3 h 2 2 6 h 4 Jubstitute 1 this x value in V V 2 - W 2 2 3h h 4 2 LY x h 3 16 3 2 3 h 16Now differentiate the 'V' with respect to t V = 3 h dv 3 x 3h x db 16 d+ we know dv , 30 um-/ sec, we have to find oh at h2 5cm , Substituting 30 - 3 x 3x ( 5 ) x dh 16 db 30x 16 1ox lb 2 3 X 3 X 25 3 X 25 2 2 x 16 32 2 = 2. 1333 3 x 5 15 Therefore Rate of Water level rising when is cm/ sec or 2.133 (m/see