A right circular cylinder has volume

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A right circular cylinder has volume V=πr2hV=\pi r^{2}h, where rr is its radius and hh its height, both measured in centimeters. At a certain instant the radius is 10 cm and increasing at 0.3 cm/min, while the height is 25 cm and decreasing at 0.5 cm/min. Which of the following statements about dVdt\displaystyle\tfrac{dV}{dt} at that instant is correct? (a) 25π cm3 ⁣/min25\pi\text{ cm}^{3}\!/\text{min} (b) 00 (c) 100π cm3 ⁣/min100\pi\text{ cm}^{3}\!/\text{min} (d) −50π cm3 ⁣/min-50\pi\text{ cm}^{3}\!/\text{min}

Related theory

Browse the problem library