A rectangular box with a square base and no top must have a volume of

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

1000\,\mathrm{cm^3}

. The material for the base costs

\$0.20

per

\mathrm{cm^2}

, and the material for the four sides costs

\$0.10

per

\mathrm{cm^2}

. What height

h

of the box minimizes the total material cost? (a)

13.3\,\mathrm{cm}

(b)

10\,\mathrm{cm}

(c)

6.3\,\mathrm{cm}

(d)

4.0\,\mathrm{cm}