# +26 Volume Of Prisms Pyramids Cylinders And Cones Worksheet Answers

## Volume of Prisms, Pyramids, Cylinders, and Cones Worksheet Answers

### Introduction

Understanding the volume of different geometric solids is a fundamental concept in mathematics. It allows us to calculate the amount of space an object occupies, which is useful in various real-life scenarios. In this worksheet, we will explore the volume of prisms, pyramids, cylinders, and cones. Let's dive in and find the answers to these exercises!

### Prisms

A prism is a three-dimensional solid with two congruent parallel bases, connected by rectangular faces. To find the volume of a prism, the formula is A(base) × h, where A(base) represents the area of the base and h is the height. Let's solve some problems:

### Prism Worksheet Answers

1. The base of a rectangular prism has dimensions 4 cm × 6 cm, and its height is 10 cm. Find the volume.

Solution: A(base) = 4 cm × 6 cm = 24 cm². Volume = 24 cm² × 10 cm = 240 cm³.

2. The base of a triangular prism has a base length of 8 cm and a height of 6 cm. The height of the prism is 12 cm. Calculate the volume.

Solution: A(base) = ½ × 8 cm × 6 cm = 24 cm². Volume = 24 cm² × 12 cm = 288 cm³.

### Pyramids

A pyramid is a three-dimensional solid with a polygonal base and triangular faces that converge at a single point called the apex. To find the volume of a pyramid, the formula is ⅓ × A(base) × h, where A(base) represents the area of the base and h is the height. Let's solve some problems:

### Pyramid Worksheet Answers

1. The base of a square pyramid has a side length of 5 cm, and its height is 8 cm. Calculate the volume.

Solution: A(base) = 5 cm × 5 cm = 25 cm². Volume = ⅓ × 25 cm² × 8 cm = 66.7 cm³ (rounded to one decimal place).

2. The base of a triangular pyramid has an area of 12 cm², and its height is 10 cm. Find the volume.

Solution: A(base) = 12 cm². Volume = ⅓ × 12 cm² × 10 cm = 40 cm³.

### Cylinders

A cylinder is a three-dimensional solid with two congruent circular bases and a curved surface connecting them. To find the volume of a cylinder, the formula is πr²h, where r represents the radius of the base and h is the height. Let's solve some problems:

### Cylinder Worksheet Answers

1. The radius of a cylinder is 3 cm, and its height is 10 cm. Calculate the volume.

Solution: Volume = π × 3 cm × 3 cm × 10 cm = 282.7 cm³ (rounded to one decimal place).

2. The diameter of a cylinder is 8 cm, and its height is 12 cm. Find the volume.

Solution: Radius = 8 cm ÷ 2 = 4 cm. Volume = π × 4 cm × 4 cm × 12 cm = 603.2 cm³ (rounded to one decimal place).

### Cones

A cone is a three-dimensional solid with a circular base and a curved surface meeting at a single point called the apex. To find the volume of a cone, the formula is ⅓ × πr²h, where r represents the radius of the base and h is the height. Let's solve some problems:

### Cone Worksheet Answers

1. The radius of a cone is 6 cm, and its height is 10 cm. Calculate the volume.

Solution: Volume = ⅓ × π × 6 cm × 6 cm × 10 cm = 376.8 cm³ (rounded to one decimal place).

2. The diameter of a cone is 12 cm, and its height is 8 cm. Find the volume.

Solution: Radius = 12 cm ÷ 2 = 6 cm. Volume = ⅓ × π × 6 cm × 6 cm × 8 cm = 301.6 cm³ (rounded to one decimal place).

### Conclusion

Calculating the volume of prisms, pyramids, cylinders, and cones is an essential skill in mathematics. By understanding these formulas and solving the provided exercises, you have gained a solid foundation in finding the volume of these geometric solids. Keep practicing and exploring the world of mathematics!