Integrated Math 3 HonorsName

Test Review– Unit 2 – Geometric Proofs and Modeling

For each 2-D shape shown below,

  1. Find the 3-D shape that would be generated if we rotate the 2-D shape about the axis given. Draw a diagram and label all known dimensions.

For this 3-D figure, find the following:

  1. Surface Area
  2. Volume
  3. Shape of the horizontal cross section (parallel to the base) half way up the figure
  4. Area & Perimeter of this horizontal cross section
  5. Shape of a vertical cross section (perpendicular to the base) passing through the center of the figure.
  6. Area & Perimeter of this horizontal cross section
  7. If the figure has a mass of 400 grams, find the density.

Figure A:Figure B:Figure C:

A = 49

  1. A roll of toilet paper is 4 inches high and has a diameter of 4 ½ inches. The cardboard inside has a diameter of 2 inches.

A.)Identify the shapes of the horizontal and vertical cross sections with the roll sitting on the base.

B.) Find the area of each of the cross sections (Vertical cross section cuts it symmetrically).

C.) What is the surface area of the toilet paper?

D.) Find the volume of the cardboard.

  1. Henry had 10 mosquito bites on his arm. His mom put a circle around the mosquito bites and found that the diameter of the circle was 4 inches wide.

A.)Find the area of the circle created by Henry’s mom.

B.)Find the density of the mosquito bites per inches2.

  1. Farmers in Field County are testing new varieties of corn to see if they can increase their crop yield per acre. They planted 452 acres with Lotsacorn and collected a total of 69,110 bushels. They also planted 396 acres with Cornaplenty, which yielded a total of 59,637 bushels. Which company produced the higher corn density? Mathematically justify your reasoning.
  1. For my son’s birthday we all wore party hats (I’m sure that wasn’t embarrassing). The hats were 5 inches tall with a base whose circumference was

A.)Classify the horizontal and vertical cross sections

( Vertical cross section cuts the cone symmetrically).

B.)Find the area of each of these cross sections.

C.)Find the slant height of the cone

D.)Find the volume of the cone

  1. The diameter of the earth is 7917.5 miles.

A.) Find the surface area of the earth

B.) Find the volume of the earth

C.) If there are 7,400,000,000 people in the world, find the earth’s density.

  1. Identify the shape you would need to rotate to obtain each of the following:

A. A cylinderB. A sphereC. A cone

  1. A Toblerone box is created using the dimensions below. Find the amount of cardboard used to create the box. Then find the volume of the chocolate the box can hold.

  1. Find the total surface area and volume of the toy house shown below.

  1. Find the total Surface Area and Volume of the Toy shown below.