Introduction
Welcome to our article on the "Filling and Wrapping Investigation 2 Answer Key". In this article, we will provide you with a comprehensive answer key for Investigation 2 of the Filling and Wrapping topic. Whether you are a student or a teacher looking for the correct answers, you've come to the right place. We have carefully analyzed and solved all the problems in Investigation 2 to help you understand the concepts better. So, let's dive in and explore the answer key for Filling and Wrapping Investigation 2!
Problem 1: Finding the Surface Area of a Rectangular Prism
In Problem 1, you are given the dimensions of a rectangular prism and asked to find its surface area. To solve this problem, you need to calculate the areas of all the six faces of the prism and then add them together. Let's break it down step by step:
Step 1: Identify the Dimensions
The first step is to identify the dimensions given in the problem. These dimensions will help us calculate the areas of the faces. In this problem, let's say the length of the prism is 5 units, the width is 3 units, and the height is 4 units.
Step 2: Calculate the Areas of the Faces
Next, we calculate the areas of the six faces of the rectangular prism. The formula to find the area of a rectangle is length multiplied by width. So, for the top and bottom faces, the area would be 5 units (length) multiplied by 3 units (width), which equals 15 square units each. Similarly, for the front and back faces, the area would be 5 units (length) multiplied by 4 units (height), which equals 20 square units each. Finally, for the side faces, the area would be 3 units (width) multiplied by 4 units (height), which equals 12 square units each.
Step 3: Add the Areas of the Faces
Once we have calculated the areas of all the faces, we simply add them together to find the total surface area of the rectangular prism. In this case, the total surface area would be 15 square units (top) + 15 square units (bottom) + 20 square units (front) + 20 square units (back) + 12 square units (left side) + 12 square units (right side), which equals 94 square units.
Problem 2: Finding the Volume of a Cylinder
In Problem 2, you are given the radius and height of a cylinder and asked to find its volume. To solve this problem, you need to use the formula for the volume of a cylinder, which is π (pi) multiplied by the square of the radius, multiplied by the height. Let's go through the steps:
Step 1: Identify the Dimensions
The first step is to identify the dimensions given in the problem. In this case, let's say the radius of the cylinder is 2 units and the height is 6 units.
Step 2: Calculate the Volume
Next, we use the formula for the volume of a cylinder to calculate the volume. The formula is π (pi) multiplied by the square of the radius, multiplied by the height. So, using the given dimensions, the volume would be π (pi) multiplied by 2 squared (4), multiplied by 6, which equals 24π cubic units.
Problem 3: Finding the Surface Area of a Cone
In Problem 3, you are given the radius and slant height of a cone and asked to find its surface area. To solve this problem, you need to use the formula for the surface area of a cone, which is π (pi) multiplied by the radius, multiplied by the sum of the radius and the slant height. Let's break it down:
Step 1: Identify the Dimensions
The first step is to identify the dimensions given in the problem. Let's say the radius of the cone is 3 units and the slant height is 5 units.
Step 2: Calculate the Surface Area
Next, we use the formula for the surface area of a cone to calculate the surface area. The formula is π (pi) multiplied by the radius, multiplied by the sum of the radius and the slant height. So, using the given dimensions, the surface area would be π (pi) multiplied by 3, multiplied by 3 + 5, which equals 24π square units.
Problem 4: Finding the Volume of a Sphere
In Problem 4, you are given the radius of a sphere and asked to find its volume. To solve this problem, you need to use the formula for the volume of a sphere, which is 4/3 multiplied by π (pi), multiplied by the cube of the radius. Let's go through the steps:
Step 1: Identify the Dimensions
The first step is to identify the dimensions given in the problem. Let's say the radius of the sphere is 4 units.
Step 2: Calculate the Volume
Next, we use the formula for the volume of a sphere to calculate the volume. The formula is 4/3 multiplied by π (pi), multiplied by the cube of the radius. So, using the given dimensions, the volume would be 4/3 multiplied by π (pi), multiplied by 4 cubed (64), which equals 268.08 cubic units.
Problem 5: Finding the Surface Area of a Pyramid
In Problem 5, you are given the base perimeter, slant height, and height of a pyramid and asked to find its surface area. To solve this problem, you need to calculate the areas of the base and the four triangular faces and then add them together. Let's break it down step by step:
Step 1: Identify the Dimensions
The first step is to identify the dimensions given in the problem. Let's say the base perimeter of the pyramid is 12 units, the slant height is 5 units, and the height is 3 units.
Step 2: Calculate the Areas
Next, we calculate the areas of the base and the four triangular faces. The formula to find the area of a triangle is base multiplied by height divided by 2. So, for the base, the area would be 12 units (base) multiplied by 3 units (height), divided by 2, which equals 18 square units. Similarly, for the four triangular faces, the area would be 5 units (base) multiplied by 3 units (height), divided by 2, which equals 7.5 square units each.
Step 3: Add the Areas
Once we have calculated the areas of all the faces, we simply add them together to find the total surface area of the pyramid. In this case, the total surface area would be 18 square units (base) + 7.5 square units (face 1) + 7.5 square units (face 2) + 7.5 square units (face 3) + 7.5 square units (face 4), which equals 48 square units.
Conclusion
That concludes our answer key for Filling and Wrapping Investigation 2. We hope this article has helped you understand how to solve various problems related to finding the surface area and volume of different geometric shapes. Remember, practice makes perfect, so keep practicing these concepts to strengthen your understanding. If you have any further questions or need clarification on any of the problems, feel free to reach out to us. Happy learning!