Solve Quadratic Equations (Factoring a=1)
2 answers:
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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>
A square pyramid is called like so because its base is a square.
notice this one, its base is a 0.4x0.4 square, and the triangular faces have a base of 0.4 and an altitude or height of 5.
so we can simply get the area of the base and all four triangular faces and sum them up, and that's the surface area of the pyramid.
![\bf \stackrel{\textit{squarish base}}{(0.4\cdot 0.4)}~~+~~\stackrel{\textit{4 triangles}}{4\left[\cfrac{1}{2}(0.4)(5) \right]}\implies 0.16~~+~~4\implies 4.16](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bsquarish%20base%7D%7D%7B%280.4%5Ccdot%200.4%29%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7B4%20triangles%7D%7D%7B4%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%280.4%29%285%29%20%20%5Cright%5D%7D%5Cimplies%200.16~~%2B~~4%5Cimplies%204.16)
notice this one, its base is a 0.4x0.4 square, and the triangular faces have a base of 0.4 and an altitude or height of 5.
so we can simply get the area of the base and all four triangular faces and sum them up, and that's the surface area of the pyramid.