MCQ with Solution: Surface Areas and Volumes - Class 9 Maths

Introduction:
In this document, we will discuss multiple-choice questions (MCQs) with solutions on the topic of surface areas and volumes in Class 9 Mathematics. These questions are designed to test your understanding of various concepts related to cones.

MCQs:
1. Which of the following statements is true?
a) A cone has only one curved surface.
b) A cone has two circular bases.
c) A cone has no vertices.
d) A cone has only one edge.

2. The total surface area of a cone is given by the formula:
a) πr²
b) πrl
c) πr(r + l)
d) 2πrl

3. The lateral surface area of a cone is given by the formula:
a) πrl
b) 2πrl
c) πr²
d) πr(r + l)

4. The volume of a cone is given by the formula:
a) 1/3πr²
b) 1/3πr(r + l)
c) 1/3πrl
d) 1/3πr³

Solutions:
1. Answer: b) A cone has two circular bases.
Explanation: A cone is a three-dimensional geometric shape with a circular base and a pointed top called the apex. Therefore, a cone has two circular bases.

2. Answer: d) 2πrl
Explanation: The total surface area of a cone is given by adding the area of the curved surface (lateral surface area) to the area of the base. The formula for the lateral surface area is πrl, and the formula for the base area is πr². Therefore, the total surface area of a cone is given by 2πrl + πr², which simplifies to 2πrl.

3. Answer: a) πrl
Explanation: The lateral surface area of a cone refers to the curved surface area excluding the base. It is given by the formula πrl, where r is the radius of the base and l is the slant height of the cone.

4. Answer: c) 1/3πrl
Explanation: The volume of a cone is given by the formula (1/3)πr²h, where r is the radius of the base and h is the height of the cone. Since the height of a cone is equal to the slant height (l) in a right cone, the formula for the volume simplifies to (1/3)πrl.

In conclusion, these MCQs and their solutions provide a comprehensive understanding of the concepts related to cones, including their surface areas and volumes.