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 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.

❖
❖
❖
❖
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) **

❖ 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.

❖ 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.

❖
❖
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) **

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

❖ 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) - x ²
3D (volume) x³

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

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

❖ 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.

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

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