Lesson 1 Any Way You Slice It Develop Understanding

Ready

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 $5 cm$ by $12 cm$ .

2.

Calculate the area of the same rectangle.

3.

Calculate the volume of a rectangular box that measures $5 cm$ by $12 cm$ and is $8 cm$ 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 $8$ inches. (Use $π = 3.14$ )

7.

Calculate the area of the circle in problem 6.

8.

Calculate the volume of a ball with a diameter of $16$ inches. $(V = \frac{4}{3} π r^{3})$

9.

Calculate the surface area of the ball in problem 8. $(S A = 4 π r^{2})$

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 $E F$ and circle $D,$ 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 $3 inches$ and a height of $8 inches$ . 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: $V = \frac{1}{3} π r^{2} h$

sphere: $V = \frac{4}{3} π r^{3}$

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 $T A S K$ is a rhombus. Show your work to justify the defining properties of the rhombus.

18.

Considering quadrilateral $T A S K$ from problem 17, provide an argument that will either prove or disprove $\overset{―}{T S} ⊥ \overset{―}{K A}$ .

19.

Use the two given points on the grid, $A (- 7, 2)$ and $B (- 4, 3)$ as two vertices of a square and locate two other points, $C$ and $D$ , for the other two vertices of the square. For a challenge, attempt to find as many possible locations for points $C$ and $D$ as possible.

20.

Given the coordinates of the quadrilateral $L I V E$ , find its perimeter. $L (5, 1)$ , $I (1, 3)$ , $V (- 3, 1)$ , $E (3, - 2)$