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Water flows into a cylindrical tank at the rate of 1000 cubic inches
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31 Dec 2024, 16:10
31 Dec 2024, 16:10
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Water flows into a cylindrical tank at the rate of 1000 cubic inches/min. If the water level rises in the tank at the rate of 0.1 inches/min, what is the radius (in inches) of the cylindrical tank?
A. \(\dfrac{25}{\sqrt{\pi}}\)
B. \(\dfrac{50}{\sqrt{\pi}}\)
C. \(\dfrac{100}{\sqrt{\pi}}\)
D. \(\dfrac{200}{\sqrt{\pi}}\)
E. \(\dfrac{400}{\sqrt{\pi}}\)
A. \(\dfrac{25}{\sqrt{\pi}}\)
B. \(\dfrac{50}{\sqrt{\pi}}\)
C. \(\dfrac{100}{\sqrt{\pi}}\)
D. \(\dfrac{200}{\sqrt{\pi}}\)
E. \(\dfrac{400}{\sqrt{\pi}}\)
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Re: Water flows into a cylindrical tank at the rate of 1000 cubic inches
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09 Jan 2025, 22:09
09 Jan 2025, 22:09
any solutions for this please? seems a little tricky
Water flows into a cylindrical tank at the rate of 1000 cubic inches
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09 Jan 2025, 23:28
09 Jan 2025, 23:28
Expert Reply
Let the radius of the cylindrical tank be ' $\(r\)$ ' inches.
It is known that the water rises 0.1 inches/min which is equal to the height of the cylindrical tank.
We know that water runs in the cylindrical tank at the rate of 1000 cubic inches/min, so we get volume of the cylindrical tank $\(\pi r^2 h=1000 \quad\)$ i.e. $\(\pi \times r^2 \times 0.1=1000 \Rightarrow r=\sqrt{1000 \times \frac{1}{\pi } \times \frac{1}{0.1}}=\)
\(\frac{100}{\sqrt{\pi}}\)$ inches
Hence the answer is (C).
It is known that the water rises 0.1 inches/min which is equal to the height of the cylindrical tank.
We know that water runs in the cylindrical tank at the rate of 1000 cubic inches/min, so we get volume of the cylindrical tank $\(\pi r^2 h=1000 \quad\)$ i.e. $\(\pi \times r^2 \times 0.1=1000 \Rightarrow r=\sqrt{1000 \times \frac{1}{\pi } \times \frac{1}{0.1}}=\)
\(\frac{100}{\sqrt{\pi}}\)$ inches
Hence the answer is (C).
