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प्रश्न
An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast will the volume of the cube increase if the edge is 5 cm long?
विकल्प
75 cm3/sec
750 cm3/sec
7500 cm3/sec
1250 cm3/sec
उत्तर
750 cm3/sec
Explanation:
Let x be edge of cube.
Given `dx/dt` = 10 cm/sec
Volume of the cube V = x3
∴ `(dV)/dt = 3x^2 dx/dt`
When x = 5 cm
`(dV)/dt` = 3 × 52 × 10
= 750 cm3/sec.
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