Volume of Sold with a Known Crosssection

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In summary, the solid formed by isosceles right triangles perpendicular to the x axis has a base bounded by x^2 + y^2 = 4. The hypotenuse of each triangle is sitting on the base of the figure. To find the area, we use the formula (1/2)bh = (1/4)y^2, where a = y√2. This was confirmed by finding a = √(1/2) * y from 2a^2 = y^2.
  • #1
mmg0789
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the base is bounded by x^2 + y^2 = 4
the solid is formed by isosceles right triangles perpendicular to x axis. the hypotenuse of each triangle is sitting on the base of the figure

i just need to know what area formula i would start out with, is it just bh/2 ?
 
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  • #2
An "isosceles right triangle perpendicular to the x axis" has hypotenuse y. Since it is isosceles, a2+ a2= 2a2= y2. That is, each leg has length [itex]a= y\sqrt{2}[/itex] and so its area is (1/2)bh= (1/2)(a*a)= (1/2)(2y)= y.
 
  • #3
hmm i found that a= sqrt(1/2) * y from 2a^2=y^2, the area would then be
(1/4)y^2. Right?
 
  • #4
mmg0789 said:
hmm i found that a= sqrt(1/2) * y from 2a^2=y^2, the area would then be
(1/4)y^2. Right?

yes, you are right.
 

What is the definition of "Volume of Sold with a Known Crosssection"?

The volume of sold with a known crosssection is a measurement of the amount of space occupied by an object or substance that has a known crosssectional shape. It is typically measured in cubic units such as centimeters cubed or liters.

What is the formula for calculating the volume of sold with a known crosssection?

The formula for calculating the volume of sold with a known crosssection depends on the shape of the crosssection. For example, the formula for calculating the volume of a cube is V = s^3, where s is the length of one side of the cube. Other common formulas include V = πr^2h for a cylinder and V = 1/3πr^2h for a cone.

Why is it important to calculate the volume of sold with a known crosssection?

Calculating the volume of sold with a known crosssection is important for a variety of reasons. It allows us to accurately measure the amount of space occupied by an object or substance, which can be useful in fields such as engineering, architecture, and chemistry. It also helps us understand the properties and characteristics of different objects and substances.

How does the volume of sold with a known crosssection differ from the volume of sold with an unknown crosssection?

The main difference between the volume of sold with a known crosssection and the volume of sold with an unknown crosssection is the level of information we have about the object or substance. With a known crosssection, we already have knowledge of the shape and dimensions of the object, making it easier to calculate the volume. With an unknown crosssection, we may have to use more complex methods such as displacement or integration to determine the volume.

What are some real-world applications of calculating the volume of sold with a known crosssection?

The calculation of the volume of sold with a known crosssection has many practical applications. In construction, it is used to determine the amount of materials needed for a project. In manufacturing, it is used to accurately measure and allocate resources. In chemistry, it is used to calculate the concentration of a solution. It is also used in fields such as medicine, geology, and environmental science.

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