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snow_tiger [21]

3 years ago

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Mathematics

2 answers:

nikklg [1K]3 years ago

8 0

The Answer is x = 8/5.

Elanso [62]3 years ago

5 0

$\bf 6-5x+6=4\implies -5x+12=4\implies \stackrel{\textit{adding 5x to both sides}}{12=4+5x}\\\\\\\stackrel{\textit{subtracting 4 to both}}{8=5x}\implies \cfrac{8}{5}=x\implies 1\frac{3}{5}=x$

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Answer:

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An empty cylindrical vase with a radius of 8 cm and a height of 9 cm is filled with 6 cm^3 of sand every 15 seconds. At the same

Andru [333]

General Idea:

The volume of cylinder is given by $\pi r^{2} h$ , where r is the radius and h is the height of the cylinder.

Applying the concept:

Step 1: We need to find the volume of full cylinder with the given dimensions using the formula.

Volume of full cylinder $=\pi r^{2} h=\pi* 8^{2} *9=576\pi cm^{3}$

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So volume of sand filled in 1 minute $= 6*4 cm^{3} = 24 cm^{3}$ .

$8 cm^{3}$ of sand taken out of cylindrical vase every minute.

Net volume of sand filled in 1 minute = Volume of sand filled in the vase in one minute - Volume of sand taken out in 1 minute

Net volume of sand filled in 1 minute $=24 cm^{3} - 8cm^{3}=16cm^{3}$

Volume of sand filled in x minutes $= 16x$ .

We need to set up an equation to find the number of minutes need to fill half the volume in cylindrical vase.

$16x = 288\pi \\ \\ x=\frac{288\pi}{16} \\ \\ x=18\pi \\ \\ x=57 minutes$

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The number of minutes required for the base be half filled with sand is 57

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