A cylindrical storage tank without a top must hold of liquid

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

A cylindrical storage tank without a top must hold 5000 ft35000\ \text{ft}^3 of liquid. Material for the base costs 1212 per square foot, and material for the curved side costs 88 per square foot. Let rr be the radius of the base in feet. Determine the radius that minimizes the total material cost, and state that minimum cost to the nearest dollar.

Related theory

Browse the problem library