# 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. , , ,