Geometric Solids Modeling Project
Intro
In class for Geometry math, we got to choose an object with at least 2 different shapes. We had to work individually. I divided my object into 7 different sections and solved for each which I combined two since they are equal so I doubled what I got for one and added every other separate section together to find volume and surface area of object I chose. I chose a wooden calendar with cubes that say the day and the at the bottom are rectangular prisms that say the months which are in Spanish. The bottom is a bit slanted so it could stand which I needed to make sure I included that so my answer can be more accurate.
Concepts
Volume- amount of space an object takes up (units cubed)
Radius- straight line from center of circle to any point on circumference or sphere
Surface Area- measurement of surface of an object
Lateral Area- measurement of sides of the surface of an object not involving base (units squared)
Area- measurement of surface (units squared)
Sector- A portion of an object
Segment- Parts which may get divided into sections (pieces)
Central Angle- Angle in the center (polygons and spheres have a way to calculate central angle for shape)
Height- How tall an object is
Base- The bottom or main side of a shape in which it is the base of the figure or shape
Formulas Used
r^2𝞹(central angle/360)=area of sector
bh/2=area of triangle
(area of sector)-(area of triangle)=(area of segment)(width)=volume of sector
(area of base)(height)=volume of prisms
Volumes added up= Volume total (units^3)
2(area of segment)+(area of curve/ lateral area)= SA segments
2(area of base)+Lateral area= SA rectangular prism
Surface areas added up= Total Surface Area (units^2)
Shapes
Depending on shape I determined how to solve. I divided my object to 7 different parts to solve in which I then added altogether in the end to get my final result. I used many tools and formulas to calculate and combined some to match what I had to solve for.
Volume and Surface Area of object (without cubes and rectangles in center):
Volume is around 7.53 inches cubed
Surface area is around 35.1 inches squared
Space for cubes and rectangles in object
Volume is around 5.08 in^3
SA≈8.13 in^2
Volume and Surface Area of cubes and rectangles separately
Rectangular prisms with months in Spanish (3):
SA≈3.32 in^2→ ≈9.96 in^2
V≈0.24 in^3 → ≈0.72 in^3
Cubes (2):
SA≈6in^2 → ≈12in^2
V≈1 in^3 → ≈2in^3
Accuracy of Answer
It is rounded and formulas were used to match and find the volume and surface area of object. I divided object into seven part which I then added all together in the end and the answer is pretty accurate although not exact. It is possible some quite human errors was made by miscalculation or measuring wrong so it might be off by a bit possibly because of that. Its not an exact answer, it is rounded. But it is pretty accurate to actual volume and surface area of the object.
Slideshow below explains calculations, how I solved and more for my solids modeling project
In class for Geometry math, we got to choose an object with at least 2 different shapes. We had to work individually. I divided my object into 7 different sections and solved for each which I combined two since they are equal so I doubled what I got for one and added every other separate section together to find volume and surface area of object I chose. I chose a wooden calendar with cubes that say the day and the at the bottom are rectangular prisms that say the months which are in Spanish. The bottom is a bit slanted so it could stand which I needed to make sure I included that so my answer can be more accurate.
Concepts
Volume- amount of space an object takes up (units cubed)
Radius- straight line from center of circle to any point on circumference or sphere
Surface Area- measurement of surface of an object
Lateral Area- measurement of sides of the surface of an object not involving base (units squared)
Area- measurement of surface (units squared)
Sector- A portion of an object
Segment- Parts which may get divided into sections (pieces)
Central Angle- Angle in the center (polygons and spheres have a way to calculate central angle for shape)
Height- How tall an object is
Base- The bottom or main side of a shape in which it is the base of the figure or shape
Formulas Used
r^2𝞹(central angle/360)=area of sector
bh/2=area of triangle
(area of sector)-(area of triangle)=(area of segment)(width)=volume of sector
(area of base)(height)=volume of prisms
Volumes added up= Volume total (units^3)
2(area of segment)+(area of curve/ lateral area)= SA segments
2(area of base)+Lateral area= SA rectangular prism
Surface areas added up= Total Surface Area (units^2)
Shapes
Depending on shape I determined how to solve. I divided my object to 7 different parts to solve in which I then added altogether in the end to get my final result. I used many tools and formulas to calculate and combined some to match what I had to solve for.
Volume and Surface Area of object (without cubes and rectangles in center):
Volume is around 7.53 inches cubed
Surface area is around 35.1 inches squared
Space for cubes and rectangles in object
Volume is around 5.08 in^3
SA≈8.13 in^2
Volume and Surface Area of cubes and rectangles separately
Rectangular prisms with months in Spanish (3):
SA≈3.32 in^2→ ≈9.96 in^2
V≈0.24 in^3 → ≈0.72 in^3
Cubes (2):
SA≈6in^2 → ≈12in^2
V≈1 in^3 → ≈2in^3
Accuracy of Answer
It is rounded and formulas were used to match and find the volume and surface area of object. I divided object into seven part which I then added all together in the end and the answer is pretty accurate although not exact. It is possible some quite human errors was made by miscalculation or measuring wrong so it might be off by a bit possibly because of that. Its not an exact answer, it is rounded. But it is pretty accurate to actual volume and surface area of the object.
Slideshow below explains calculations, how I solved and more for my solids modeling project
Reflection
Two things I did well was figuring out how to calculate the segment of the almost semi circle volume and surface area part of object and another is how I organized my work showing how I calculated. Two things that did not go so well is how I ended up doing a majority of this project last minute and how I could not get an exact answer or calculate so actual exact volume and surface area ends up being around what was calculated. Overall, the project was fun.
Two things I did well was figuring out how to calculate the segment of the almost semi circle volume and surface area part of object and another is how I organized my work showing how I calculated. Two things that did not go so well is how I ended up doing a majority of this project last minute and how I could not get an exact answer or calculate so actual exact volume and surface area ends up being around what was calculated. Overall, the project was fun.