Step by step solution to "The volume of a cube is increasing at..."

High School
Geometry
High school geometry
Solid Geometry

Sinead Mcgee

Answered question

2021-08-09

The volume of a cube is increasing at the rate of 1200 cm³/min at the instant its edges are 20 cm long. At what rate are the edges changing at that instant?

Answer & Explanation

Alix Ortiz

Skilled2021-08-10Added 109 answers

The volume of a cube with edge length ee is given by:
$V = e^{3}$
Differentiate with respect to t: $\frac{d V}{d t} = 3 e^{2} \frac{d e}{d t}$
Substitute $\frac{d V}{d t} = 1200 c m^{3} / m i n$ and e=20 cm then solve for de/dt: $1200 = 3 {(20)}^{2} \cdot (\frac{d e}{d t})$
$1200 = 1200 (\frac{d e}{d t})$
$1 = \frac{d e}{d t}$
or
$\frac{d e}{d t} = 1 \frac{c m}{min}$

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