# +26 Course 1 Chapter 10 Volume And Surface Area Answer Key

## Introduction

In this article, we will provide you with the answer key for Course 1, Chapter 10 on volume and surface area. This chapter focuses on the fundamental concepts and formulas related to calculating the volume and surface area of various geometric shapes. By understanding these concepts and using the provided answer key, you will be able to check your answers and gain a better understanding of the topic.

### Section 1: Volume of Rectangular Prisms

In this section, we will cover the formula for finding the volume of rectangular prisms. A rectangular prism is a three-dimensional shape with six rectangular faces. To calculate its volume, you multiply the length, width, and height of the prism. For example, if a rectangular prism has a length of 5 units, a width of 3 units, and a height of 4 units, the volume would be 5 * 3 * 4 = 60 cubic units.

### Section 2: Surface Area of Rectangular Prisms

In this section, we will explore the formula for finding the surface area of rectangular prisms. The surface area is the total area of all the faces of the prism. To calculate it, you multiply the length times the width of each face and then sum up the areas. For example, if a rectangular prism has a length of 5 units, a width of 3 units, and a height of 4 units, the surface area would be 2(5 * 3) + 2(5 * 4) + 2(3 * 4) = 94 square units.

### Section 3: Volume of Triangular Prisms

In this section, we will discuss the formula for finding the volume of triangular prisms. A triangular prism is a three-dimensional shape with two triangular bases and three rectangular faces. To calculate its volume, you multiply the area of the triangular base by the height of the prism. For example, if a triangular prism has a base with a height of 6 units and a height of 8 units, the volume would be 1/2 * 6 * 8 = 24 cubic units.

### Section 4: Surface Area of Triangular Prisms

In this section, we will cover the formula for finding the surface area of triangular prisms. The surface area is the total area of all the faces of the prism. To calculate it, you find the sum of the areas of the two triangular bases and the three rectangular faces. For example, if a triangular prism has a base with a height of 6 units and a height of 8 units, the surface area would be 2(1/2 * 6 * 8) + 3(6 * 8) = 144 square units.

### Section 5: Volume of Cylinders

In this section, we will discuss the formula for finding the volume of cylinders. A cylinder is a three-dimensional shape with two circular bases and a curved surface. To calculate its volume, you multiply the area of the circular base by the height of the cylinder. For example, if a cylinder has a radius of 4 units and a height of 6 units, the volume would be π * 4^2 * 6 = 301.44 cubic units (rounded to two decimal places).

### Section 6: Surface Area of Cylinders

In this section, we will cover the formula for finding the surface area of cylinders. The surface area is the sum of the areas of the two circular bases and the curved surface. To calculate it, you find the sum of the areas of the two circular bases and the area of the curved surface, which is the circumference of the base multiplied by the height of the cylinder. For example, if a cylinder has a radius of 4 units and a height of 6 units, the surface area would be 2(π * 4^2) + 2π * 4 * 6 = 301.44 square units (rounded to two decimal places).

### Section 7: Volume of Cones

In this section, we will discuss the formula for finding the volume of cones. A cone is a three-dimensional shape with a circular base and a curved surface that tapers to a point called the vertex. To calculate its volume, you multiply the area of the circular base by the height of the cone and divide it by 3. For example, if a cone has a radius of 5 units and a height of 8 units, the volume would be 1/3 * π * 5^2 * 8 = 209.44 cubic units (rounded to two decimal places).

### Section 8: Surface Area of Cones

In this section, we will cover the formula for finding the surface area of cones. The surface area is the sum of the area of the circular base and the area of the curved surface. To calculate it, you find the sum of the area of the circular base and the area of the curved surface, which is the circumference of the base multiplied by the slant height of the cone. For example, if a cone has a radius of 5 units and a slant height of 10 units, the surface area would be π * 5^2 + π * 5 * 10 = 235.62 square units (rounded to two decimal places).

### Section 9: Volume of Spheres

In this section, we will discuss the formula for finding the volume of spheres. A sphere is a three-dimensional shape with all points equidistant from its center. To calculate its volume, you multiply 4/3 by π by the radius cubed. For example, if a sphere has a radius of 6 units, the volume would be 4/3 * π * 6^3 = 904.78 cubic units (rounded to two decimal places).

### Section 10: Surface Area of Spheres

In this section, we will cover the formula for finding the surface area of spheres. The surface area is the total area of the curved surface of the sphere. To calculate it, you multiply 4 by π by the radius squared. For example, if a sphere has a radius of 6 units, the surface area would be 4 * π * 6^2 = 452.39 square units (rounded to two decimal places).

## Conclusion

By understanding the formulas and concepts discussed in this chapter, you can confidently calculate the volume and surface area of various geometric shapes. The provided answer key will help you check your answers and further reinforce your understanding. Practice using these formulas and keep exploring the world of geometry to enhance your mathematical knowledge and problem-solving skills.