Question
An edge of a variable cube is increasing at the rate of
2 cm/s. How fast is the volume of the cube increasing when the edge is 12 cm long?Solution
Let x be the length of a side and V be the volume of the cube. Then, v = x3. dV/dt = 3x2 × dx/dt It is given that dx/dt = 2 cm/s dv/dt = 3x2(2) = 6x2 Thus, when x = 12 cm dv/dt = 6 (12)2 = 864 cm3/s
In a 400-metre race, ‘A’ beats ‘B’ by 20 seconds or 80 metres. Find the time taken by ‘B’ to finish the race.
'A' and 'B' are running on a circular track of length 3600 metres. 'A' is running clockwise at 4 m/s while 'B' is running anti-clockwise at 6 m/s. Find ...
A cheetah can catch a deer running with a speed of 144 km/h and is 50 meters ahead of it, in 10 seconds. Find the time taken by the cheetah to catch a z...
A dog is 1,500 metres ahead of a man when the man starts chasing by running at 18 m/s. If the dog is running at 10 m/s, then find the time taken by the...
If a man covers a distance in 1 hour, walking at a speed of 5 km/hr, how long will it take him to cover 15 km?
- Two runners, ‘M’ and ‘N’, started from opposite ends of a track towards each other at the same time. When they met after 3 hours, runner ‘N’ ha...
A car can travel 320 kilometers in 8 hours. If a bike travels at a speed that is (3/16)th that of the car, how far will the bike go in 2 hours?
Riya rides a bike at an average speed of 50 kmph and reaches her destination in 6 hours. Himani covers the same distance in 5 hrs. If Riya increases her...
Two trains, A and B, start from two stations 240 km apart at the same time. Train A travels at 60 km/h and Train B travels at 40 km/h. After how much ti...
Ajay and Vishal left the place ‘X’ with different speeds which are in the ratio 3:2 respectively. Ajay left the place 42 seconds after Vishal. If af...
Relevant for Exams:
