alleryWater is poured at $36\,\text{m}^3/\text{s}$ into a cylindrical vessel of base radius 3 m. The rate at which water level rises is:
A1 m/s
B$\dfrac{36}{9\pi}$ m/s = $\dfrac{4}{\pi}$ m/s
C$36\pi$ m/s
D$9\pi$ m/s
Answer & Solution
Correct answer: B. $\dfrac{36}{9\pi}$ m/s = $\dfrac{4}{\pi}$ m/s
$V = \pi r^2 h$ (cylinder, $r$ constant).
$dV/dt = \pi r^2 \, dh/dt$ ⇒ $dh/dt = 36/(\pi \cdot 9) = 4/\pi$ m/s.
Keep practising Unit 4-5: Applications of Derivatives & Curve Sketching
Browse all Unit 4-5: Applications of Derivatives & Curve Sketching questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
If the tangent to the curve $y = e^{2x}$ at point $(a, e^{2a})$ passes through origin, theIf $f(x) = x^x$ for $x > 0$, then $f$ has a minimum at $x = $:The function $f(x) = \dfrac{x}{1 + x^2}$ attains its maximum value on $[0, \infty)$ at:Find the **shortest distance** from origin to the curve $xy = 4$ (in the first quadrant):A rectangle is inscribed in a semicircle of radius $R$ with base on the diameter. The **maThe function $f(x) = x^3 - 3x + 1$ has critical points at:$f(x) = 2x^3 - 3x^2 - 12x + 5$. The **local maximum value** occurs at:Find the approximate value of $ qrt{25.5}$ using differentials (given $ qrt{25} = 5$):