Estimate the value of \frac{\sqrt{2\pi }}{\sqrt{5}}
1 answer:
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Answer: third option 268.8
Explanation:
For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.
I have attached the figure for better understanding.
1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.
So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.
This is how you calculate the volume of the top portion:
1) The height of the cylinder is 54 mm - 18 mm = 36 mm
2) The formula for the volume of a cylinder is V = π (radius)^2 * height
radius = 8 mm
height = 36 mm
=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3
3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height
radius = 8 mm
height = 18 mm
V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3
4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:
Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3
5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:
time in seconds = total volume of sand / rate of dripping
time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s
That is the answer: 268.8 s
</span>
Explanation:
For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.
I have attached the figure for better understanding.
1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.
So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.
This is how you calculate the volume of the top portion:
1) The height of the cylinder is 54 mm - 18 mm = 36 mm
2) The formula for the volume of a cylinder is V = π (radius)^2 * height
radius = 8 mm
height = 36 mm
=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3
3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height
radius = 8 mm
height = 18 mm
V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3
4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:
Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3
5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:
time in seconds = total volume of sand / rate of dripping
time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s
That is the answer: 268.8 s
</span>
Answer:
Step-by-step explanation:
I suggest looking lessons on it online if you don't understand... It's hard to do your work especially if you don't understand it. Or if your online, go to past lessons or something.