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The volume of a cube is increasing at the rate of 8cm^3/sec. How fast is the surface area increasing when the length of an edge is 12cm?

Posted by Jasveer Gangwar 4 years, 4 months ago

CBSE > Class 12 > Mathematics

1 answers

Yogita Ingle 4 years, 4 months ago

volume of cube is increasing at the rate of 8cm³/s. e.g.,
edge length , a = 12cm

we know volume of cube , V = a³
now differentiate with respect to time,

put a = 12cm and dV/dt = 8cm³/s
now, 8 = 3(12)² da/dt
8 = 3 × 144 × da/dt
=> da/dt = 1/54 cm/s -----(1)

we also know surface area of cube , A = 6a²
differentiate A with respect to time,
dA/dt = 12a da/dt

put a = 12cm and from equation (1),
so, dA/dt = 12 × 12 × 1/54 = 144/54 = 8/3

hence, rate of change of surface area of cube is

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