Chapter 12 Test Geometry Answers: A Comprehensive Guide

Geometry is a branch of mathematics that deals with the study of shapes, sizes, and positions of objects. Geometry has far-ranging applications in various fields such as architecture, engineering, art, physics, and many more. A solid understanding of geometry is necessary for anyone who wants to excel in these fields. In this article, we will be discussing the Chapter 12 Test Geometry Answers in detail.

Chapter 12 in Geometry usually covers surface area and volume of different three-dimensional figures. The test is designed to measure the understanding of the student in the topic. The test consists of multiple-choice questions, short-answer questions, and even problems that involve calculations. It is important to note that the test is designed to be challenging, so it is essential to prepare well in advance.

To make things easier for you, we have compiled the questions and answers for Chapter 12 Test Geometry. This article will provide you with a comprehensive guide that will help you understand and review the concepts and questions in Chapter 12 Test Geometry.

Multiple-Choice Questions

Question #1

What type of prism is shown below?

[insert image of a triangular prism]

a) Rectangular Prism

b) Triangular Prism

c) Pentagonal Prism

d) Hexagonal Prism

Answer: b) Triangular Prism

Explanation: A triangular prism is defined as a three-dimensional figure that has two parallel triangular bases and three rectangular faces.

Question #2

What is the volume of the prism shown below?

[insert image of a rectangular prism with a height of 5cm, width of 3cm, and length of 8cm]

a) 15 cm^3

b) 36 cm^3

c) 120 cm^3

d) 132 cm^3

Answer: b) 36 cm^3

Explanation: The volume of a rectangular prism is given by the formula V=l*w*h. Therefore, the volume of the prism is 8*3*5= 120cm^3.

Question #3

What is the total surface area of the cylinder shown below?

[insert image of a cylinder with a radius of 5cm and a height of 10cm]

a) 471 cm^2

b) 314 cm^2

c) 707 cm^2

d) 157 cm^2

Answer: a) 471 cm^2

Explanation: The total surface area of a cylinder is given by the formula, TSA= 2πr(r+h). Therefore, the total surface area of the given cylinder is 2*3.14*5*10+2*3.14*5*5=471 cm^2.

Short-Answer Questions

Question #4

Calculate the surface area of the cube shown below?

[insert image of a cube with an edge of 5cm]

Answer: The surface area of a cube is given by the formula 6s^2, where s is the length of the edge. Therefore, the surface area of the given cube is 6*5^2= 150 cm^2.

Question #5

What is the volume of the square pyramid shown below?

[insert image of a square pyramid with a base length of 8cm and a height of 4cm]

Answer: The volume of a square pyramid is given by the formula V = (l^2h)/3, where l is the base length and h is the height. Therefore, the volume of the given square pyramid is (8^2*4)/3= 85.33 cm^3.

Question #6

Calculate the total surface area of the cone shown below?

[insert image of a cone with a base radius of 3cm and a height of 7cm]

Answer: The total surface area of a cone is given by the formula, TSA= πr^2+ πrl, where r is the base radius and l is the slant height. Therefore, the total surface area of the given cone is 3.14*3^2+ 3.14*3*7= 87.96 cm^2.

Problems Involving Calculations

Question #7

What is the volume of the sphere shown below?

[insert image of a sphere with a radius of 6cm]

Answer: The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius. Therefore, the volume of the sphere is (4/3)*3.14*6^3= 904.32 cm^3.

Question #8

Find the surface area of the frustum shown below?

[insert image of a frustum with a small radius of 5cm, a large radius of 8cm, and a height of 10cm]

Answer: The surface area of a frustum is given by the formula, A = π (r_1+r_2)l, where l is the slant height. To find the slant height, we need to use the Pythagorean theorem. Therefore, l =√(h^2+ (r2 − r1)^2) =√(10^2+ (8 − 5)^2) = √(122). Hence, The surface area of the frustum is π (5 + 8)√(122) = 351.47 cm^2.

Question #9

What is the height of the cylinder whose volume is 200cm^3 and its radius is 4cm?

Answer: The volume of a cylinder is given by the formula V = πr^2h. Therefore, h = V/(πr^2)= 200/(3.14*4^2)= 3.18 cm.

Question #10

What is the volume of the rectangular pyramid shown below?

[insert image of a rectangular pyramid with a base length of 6cm, a base width of 3cm, and a height of 8cm]

Answer: The volume of a rectangular pyramid is given by the formula V = (lwh)/3. Therefore, the volume of the given pyramid is (6*3*8)/3 = 48 cm^3.

Conclusion

Chapter 12 Test Geometry involves the surface area and volume of different three-dimensional shapes. The test is designed to measure the understanding of the student in the topic. The questions in the test are divided into multiple-choice questions, short-answer questions, and problems involving calculations. It is crucial to prepare well in advance to score well in the test. This guide provides you with a comprehensive understanding and answers to the questions asked in the Chapter 12 Test Geometry. We hope that this guide will help you to understand the concepts better and score higher in your test.