Water runs into a conical tank at the rate 9text ft3/textminutes. The | Basic Mathematics 0

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Water runs into a conical tank at the rate $9\text{ ft}^3/\text{minutes}$ . The tank stands point down and has a height of $10\text{ ft}$ and a base radius of $5\text{ ft}$ . How fast is the water level rising when the water is $6\text{ ft}$ deep? [5]

Water runs into a conical tank at the rate $9\text{ ft}^3/\text{minutes}$. The tank stands point down and has a height of $10\text{ ft}$ and a base radius of $5\text{ ft}$. How fast is the water level rising when the water is $6\text{ ft}$ deep? [5]

Inflow rate: $\dfrac{dV}{dt} = 9 \text{ ft}^3/\text{min}$ - Cone, point down: height $H = 10$ ft, base radius $R = 5$ ft - Find: $\dfrac{dh}{dt}$ when $h = 6$ ft Step 1: Volume of a cone $V = \frac{1}{3}\pi r^2 h$ Step 2: Similar triangles $$\frac{r}{h} = \frac{R}{H} = \frac{5}{10} = \frac{1}...

Inflow rate: $\dfrac{dV}{dt} = 9 \text{ ft}^3/\text{min}$ - Cone, point down: height $H = 10$ ft, base radius $R = 5$ ft - Find: $\dfrac{dh}{dt}$ when $h = 6$ ft Step 1: Volume of a cone $$V = \frac{1}{3}\pi r^2 h$$ Step 2: Similar triangles $$\frac{r}{h} = \frac{R}{H} = \frac{5}{10} = \frac{1}...

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Water runs into a conical tank at the rate 9text ft3/textminutes. The tank stands point down and has a height of 10text ft and a base radius of 5text ft. How fast is the water level rising when the water is 6text ft deep?