MATH Solids

SOLIDS CIRCUMFERENCE, AREA, AND VOLUME

MARÍA ISABEL MILADEH AND GABRIELA VERAS

Mathematical Edition

TABLE OF CONTENT SOLIDS | Mathematical edition

#1

Circumference and Arc lengths of a circle

#2

Areas of Circles and Sectors

#3

Sale: Queen Record

#4

Area of Polygons

#5 Sale: House

#6

Spheres

#7

Prism

#8

Cylinder

#9

Cone

#10

Pyramids

#11

Game: Crossword

#12 Sephora

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(

Arc

Radius Diameter Circumference and Arc Lengths of a Circle The circumference of a circle is the distance around the outside of the circle. It is like the perimeter of other shapes like squares. You can think of it as the line that defines the shape. For shapes made of straight edges this line is called the perimeter but for circles this defining line is called the circumference.

A circle is 360° all the way around; therefore, if you divide an arc's degree measure by 360°, you find the fraction of the circle'scircumference that the arc makes up. Then, if you multiply the length all the way around the circle (the circle's circumference) by that fraction, you get the length along the arc.

Circumference Formula = 2πr Arc Length Formula = Arc Measure/360° x Circumference

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Areas of Circles and Sectors The area of a circle is the number of square units inside that circle.

Formula: πr^2 You can work out the Area of a Sector by comparing its angle to the angle of a full circle.

Formula: Area of Sector = (θ × π)/360 × r^2 θ being the measure of the central angle.

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SALE!

Selling Queen Records 2 x 1!

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Area of a Polygon -

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AREA OF A RHOMBUS OR A KITE Despite how different they are, when it comes to area, we will see that rhombuses and kites are quite similar. The areas of rhombuses and kites are equal to one half the product of their diagonals.

Mathematically, we express this as: A = 1/2(d1 x d2), where A is the area of the of the quadrilaterals (in square units), d1 is the length of one diagonal, and d2 is the length of the other diagonal.

AREA OF A REGULAR POLYGON A regular polygon is equilateral (it has equal sides) and equiangular (it has equal angles). To find the area of a regular polygon, you use an apothem — a segment that joins the polygon’s center to the midpoint of any side and that is perpendicular to that side. The area of a polygon is half the product of the apothem times the perimeter of the figure (side length x the amount of sides).

Formula: A = 1/2 (a x P)

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SALE -

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Composite Figures

$599,999 HOUSE 3 bedrooms, 4 bathrooms, kitchen, patio with a pool and more.

Spheres It is a geometrical 3D object, that is the surface of a ball

Area: A= 4Ď€r2

r

Volume

d

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V= 4/3 πr3

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Prisms: Is a polyhedron with two parallel faces called bases. The other figures are always parallelograms.

h

B

VOLUME V= Bh

AREA In order to find the area, one must find the individual area of the bases and the other parallelograms that compose the prism. After one has found all the individual area, one needs to add them together, to find the complete area of the prism.

Cylinders Information:

Volume

It is a solid that has

V= Bh= πr2h

two parallel (usually

h

circular) bases that are connected by a curved surface.

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B

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Information:

Cone

In 1992, Barcelona gained international recognition by hosting the Olympic games which brought a massive upturn in its tourism industry. This had the effect of changing the city in ways that are still felt today with neighbourhoods renovated (and in some cases leveled) and the intense focus of modern design permeating all aspects of life in Barcelona from public buildings to something as simple as a park bench or an event poster.

Volume V= 1/3Bh= 1/3πr2h

ℓ h

Area A=πr2h + πrrℓ

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B

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P Y R A M I D S What are they?

Pyramids are polyhedrons. The base can be a polygon and they have three or more triangular faces that young at a point called apex.

The triangular sides could alos be called lateral faces.

h B

Volume V= 1/3Bh

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Crossword Puzzle

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