2) The length of the edges of a metal cuboid are increasing at a rate of 2.0 × 1

Question

2) The length of the edges of a metal cuboid are increasing at a rate of 2.0 × 10-2 mm/sec due to submersion into a heat bath. At what rate does the volume of the cuboid increase at a time when the dimensions of the cuboid are 2,4 and 7 cm respectively? [9 marks 3) An object M is rotating at a constant (counterclockwise) angular speed of 1 rad/s on a circle of radius 30 cm. The shadow of the object is projected on a straight line d, which is 50 centimeters away from the center of the circle, by a source S of light located at the center of the circle (Both the circle and the straight line are on the same plane.) What is the speed of the shadow M' when the angle travelled by M, measured with respect to the line d', which is perpendicular to line d and passes through the center of the circle, is one radian? (The following drawing in not to scale.)[10 marks] d'

Explanation / Answer

Sol:

Volume of cuboid

V=l×b×have

Rate of change in Vietnam

dv/dt=d/dt (l×b×h)

=l d/dt (b×h)+b×h dl/dt

=lb dh/dt+lh db/dt +bh dl/dt

=2×4×2×10-2+2×7×2×10-2+4×7×2×10-2

=(16+28+56)10-2

=100×10-2

=102-2

  =1 mm3/sec

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