Surface Area, Volume and Scale Factor Review Learning Target: I can use the surface area and volume formulas of cylinders, pyramids, cones and spheres to solve applied problems. Surface Area, Volume and Scale Factor Review 1. Review of Surface Area 2. Review of Volume 3. Review of Scale Factor 4. Work on Embedded Assessments

Surface Area Surface Area is the measurement of the entire area of the outside surfaces of a solid. To calculate the surface area, you need to find the area of all of the flat 2D “faces” and add them together. These “faces” are usually made up of 2D bases (B) and lateral (side) faces.

Surface Area B = Base Area - the 2D area of the top and bottom shape P = Perimeter - the distance around the base h = height - distance between the two bases h = slant height - distance diagonally along the outside The two main surface area formulas are: Prisms and Cylinders = 2B + (P)(h) Cones and Pyramids = 1B + 1/2 (P)(h) ** Remember, B changes to match the shape of the base. Ex. if B is a regular polygon, B= 1/2(n)(a)(s) **

Surface Area - Tricks Sometimes, you may need to use Pythagorean Theorem to find the slant height if given the height, (and vice versa!) For cylinders and cones, B = πr² and P = 2πr where r = radius.

Embedded Assessment

Volume Volume is the measurement of the space inside a solid figure. To calculate volume, you need to determine the area of one of the bases, and multiply it by the height. Just like in surface area, the area of the bases are 2D figures.

Volume B = Base Area - the 2D area of the top and bottom shape h = height - distance straight up to the top The two main volume formulas are: Prisms and Cylinders = (B)(h) Cones and Pyramids = 1/3(B)(h) ** Note for volume we do not use the slant height! (However, we may have to use Pythagorean Theorem to calculate the height if given the slant height) **

Spheres: Surface Area and Volume The special formulas for a sphere are: Surface Area = 4πr² Volume = 4/3πr³

Embedded Assessment

Scale Factor The scale factor is how many times a figure has increased or decreased in size. The scale factor is different when applied to a line, an area or a volume. When enlarged or shrunk measurements are multiplied like in area or volume, the effect of the scale factor is squared, or cubed. Scale Factor, if “x” is the times increased or decreased: 1D (line) - x 2D (area) - x² 3D (volume) - x³

Embedded Assessment

DO NOW 6/1: (Finals Review) Learning Target: I can use the surface area and volume formulas of cylinders, pyramids, cones and spheres to solve applied problems. DO NOW 6/1: (Finals Review) Solve for x. Model Robot Projects 1. Do Now (Finals Review) 2. Embedded Assessment Review 3. Test Review 4. Work on Robot Projects

DO NOW 6/3: (Finals Review) Learning Target: I can use the surface area and volume formulas of cylinders, pyramids, cones and spheres to solve applied problems. DO NOW 6/3: (Finals Review) Model Robot Projects 1. Do Now (Finals Review) 2. Work on Robot Projects

Model Robot: Spherical Head

2nd Semester Geometry Exhibition Student B 2nd Semester Geometry Exhibition

Scale Factors 1D- 1.2 2D-1.44 (1.2^2) 3D-1.728 (1.2^3) To find the scale factor for each one you multiply by the number of dimensions.

Price Cost=$0.02 per centimeter 1144.48x0.02= 22.9x1.2^2 / 1.2^2=1.44 Surface Area Cost=$0.02 per centimeter 1144.48x0.02= 22.9x1.2^2 / 1.2^2=1.44 22.9x1.44= Total=$32.92 Volume Cost=$0.03 per cubic centimeter 1332.28x0.03= 39.97x1.2^3 / 1.2^3= 1.728 39.97x1.728= Total=$69.06

Newer Model Measurements Head Arms Radius-3cm (2x3.14x1.2)= 3.6cm Radius-1cm (2x3.14x1.2)=1.54cm Height-x (2x3.14x1.2)=7.54cm Height-8cm (2x3.14x1.2)=9.6cm Torso Legs Radius-5cm (x1.2)=6cm Radius-4cm (x1.2)=4.8cm Height-10cm (x1.2)=12cm Height-12cm (x1.2)=14.4cm