Lesson 1Any Way You Slice ItDevelop Understanding

As you solve each problem, make certain you label the units on each of your answers.

1.

Calculate the perimeter of a rectangle that measures by .

2.

Calculate the area of the same rectangle.

3.

Calculate the volume of a rectangular box that measures by and is deep.

4.

Look back at problems 1–3. Explain how the units change for each answer.

5.

Calculate the surface area for the box in problem 3. Assume it does NOT have a cover on top. Identify the units for the surface area. How do you know your units are correct?

6.

Calculate the circumference of a circle if the radius measures inches. (Use )

7.

Calculate the area of the circle in problem 6.

8.

Calculate the volume of a ball with a diameter of inches.

9.

Calculate the surface area of the ball in problem 8.

10.

If a measurement were given, could you know if it represented a perimeter, an area, or a volume? Explain.

11.

In problems 1–9, which type of measurement would be considered a “linear measurement?”

Set

Consider the intersection of a plane and a cone.

12.

If the plane were parallel to the base of the cone, what would be the shape of the cross-section? Can you think of two possibilities? Explain.

13.

If the plane intersected the cone on a slant, so that it intersected segment and circle what would be the shape of the cross-section?

14.

Describe how the plane would need to intersect the cone in order to get a cross-section that is a triangle. Would the triangle be scalene, isosceles, or equilateral? Explain.

15.

Would it be possible for the intersection of a plane and a cone to be a line? Explain.

16.

A large waffle cone has a diameter of and a height of . Two scoops of ice cream have been stacked on top of the cone, after it was filled. The scoops are completely round and have a diameter the same as the cone.

 cone: $V=\frac{1}{3}\pi {r}^{2}h$ sphere: $V=\frac{4}{3}\pi {r}^{3}$

Find the volume of the two scoops of ice cream combined with the ice cream inside the cone.

Go

17.

Determine whether or not quadrilateral is a rhombus. Show your work to justify the defining properties of the rhombus.

18.

Considering quadrilateral from problem 17, provide an argument that will either prove or disprove .

19.

Use the two given points on the grid, and as two vertices of a square and locate two other points, and , for the other two vertices of the square. For a challenge, attempt to find as many possible locations for points and as possible.

20.

Given the coordinates of the quadrilateral , find its perimeter. , , ,