An edge of a variable cube is increasing at the rate of 10 cm / s. How fast the volume of the cube will increase when the edge is 5 cm long?

Question

An edge of a variable cube is increasing at the rate of 10 cm / s. How fast the volume of the cube will increase when the edge is 5 cm long? (A) 750 cm 3 / s (B) 75 cm 3 / s (C) 300 cm 3 / s (D) 150 cm 3 / s

Tardigrade Admin · Accepted Answer

Let l be the length of an edge and V be the volume of cube at any timet. ∵ V =l3 ∴ (d V/d t) =3 l2 (d l/d t) =3 × 52 × 10 cm 3 / s =750 cm 3 / s

Q. An edge of a variable cube is increasing at the rate of $10 c m / s$ . How fast the volume of the cube will increase when the edge is $5 c m$ long?

$750 c m^{3} / s$

$75 c m^{3} / s$

$300 c m^{3} / s$

$150 c m^{3} / s$

Let $l$ be the length of an edge and $V$ be the volume of cube at any timet.
$∵ V = l^{3}$
$∴ \frac{d V}{d t} = 3 l^{2} \frac{d l}{d t}$
$= 3 \times 5^{2} \times 10 c m^{3} / s$
$= 750 c m^{3} / s$

Q. An edge of a variable cube is increasing at the rate of 10cm/s. How fast the volume of the cube will increase when the edge is 5cm long?

750cm3/s

75cm3/s

300cm3/s

150cm3/s