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kirill [66]
3 years ago
14

What is the volume of the square pyramid with the base edges 24 ft and height

Mathematics
1 answer:
liberstina [14]3 years ago
8 0

Answer:

A

Step-by-step explanation:

The volume of a pyramid is one third the height times the area of the base.

V = ⅓ h A

The base is a square, so the area is the width times length.

V = ⅓ h wl

Problem is, we don't know the height, only the slant length.  But we can use this to find the height.

If we cut a cross section down the middle of the pyramid, we get an isosceles triangle.  The base of the triangle is 24, and the legs are 37.

If we cut this triangle in half, we get two right triangles.  Each right triangle has a base of 12 and a hypotenuse of 37.

Now we can use Pythagorean theorem to find the height of the triangle, which is also the height of the pyramid.

c² = a² + b²

37² = 12² + h²

h = 35

Now we can find the volume.  h = 35, w = 24, and l = 24:

V = ⅓ h wl

V = ⅓ (35) (24) (24)

V = 6720

So the volume is 6720 ft³, or answer A.

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Given radius (R) = 13

Diameter =  2R =  26

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Step-by-step explanation:

While a circle, symbolically, represents many different things to many different groups of people including concepts such as eternity, timelessness, and totality, a circle by definition is a simple closed shape. It is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. The distance between any point of a circle and the center of a circle is called its radius, while the diameter of a circle is defined as the largest distance between any two points on a circle. Essentially, the diameter is twice the radius, as the largest distance between two points on a circle has to be a line segment through the center of a circle. The circumference of a circle can be defined as the distance around the circle, or the length of a circuit along the circle. All of these values are related through the mathematical constant π, or pi, which is the ratio of a circle's circumference to its diameter, and is approximately 3.14159. π is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as 22/7) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero, polynomial that has rational coefficients. Interestingly, the proof by Ferdinand von Lindemann in 1880 that π is transcendental finally put an end to the millennia-old quest that began with ancient geometers of "squaring the circle." This involved attempting to construct a square with the same area as a given circle within a finite number of steps, only using a compass and straightedge. While it is now known that this is impossible, and imagining the ardent efforts of flustered ancient geometers attempting the impossible by candlelight might evoke a ludicrous image, it is important to remember that it is thanks to people like these that so many mathematical concepts are well defined today.

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