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If the edge of a cube increases at the r...

If the edge of a cube increases at the rate of 60 cm per second, at what rate the volume is increasing when the edge is 90 cm

A

486000 cu cm per sec

B

1458000cu cm per sec

C

43740000cu cm per sec

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(da)/(dt)=60(cm)/(sec)`, where a is edge and t is time.
`V=a^(3)`
`(dV)/(dt)=3a^(2)(da)/(dt)=3a^(2)xx60=180a^(2)=180xx(90)^(2)`
`=1458000(cm^(3))/(sec)`.
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