RD Sharma Class 9 Chapter 19 Solutions (Surface Area And Volume of a Right Circular Cylinder)
RD Sharma Solutions for Class 9 Maths Chapter 19 will let you learn and understand about Surface Area and Volume of a Right Circular Cylinder. There are 4 exercises in this chapter of RD Sharma Solutions which has a total of 70 questions. These questions require very short, short, long answer types and there is one exercise which is objective type questions. The questions are based on the fundamentals of right circular cylinders and you would learn about some of the basic terms associated with this like base, height, radius, axis, lateral surface, etc. You would need to apply formulas to calculate surface area and volume of right circular and hollow cylinders.
Solving these questions lets you assess how prepared you are on this topic for the purpose of exams and other medical and engineering entrance exams. Our team of subject matter experts have provided step by step explanations for these problems which will help you immensely in strengthening your foundation.
Concepts covered in this book are very important to understand the topic thoroughly and our expert’s team makes sure you get the most accurate solutions for these questions. The answers are formulated after extensive research and follow guidelines laid by CBSE hence very apt from exams point of view.
Important Topics for RD Sharma Solutions for Class 9 Chapter 19: Surface Area and Volume of a Right Circular Cylinder
A right circular cylinder is different from a general cylinder. A cylinder is a prism-shaped object which has its base in circular shape while a right circular cylinder is a cylinder whose elements are perpendicular to its base and the bases are parallel to each other.
When you rotate a rectangle along with one of its sides as an axis, it forms a right circular cylinder.
We will see definitions and formula used to solve problems related to a right circular cylinder:
- Axis – The straight line which joins the centre of the 2 bases of the cylinder is known as its axis. All points on the closed circular surface are equidistant from the axis.
- Lateral surface – The curved surface joining the 2 circular bases is the lateral surface of a right circular cylinder.
- Curved surface area – If r is the radius and h is the height of the cylinder then:
Curved surface area = 2πrh
- Total surface area – The sum of the 2 bases and the curved surface area gives the total surface area of the cylinder.
Total surface area = 2πrh + 2πr2
- Volume – This is given by multiplying the area of one of the bases with its height.
Volume = πr2h
- A hollow cylinder – A cylinder which is empty from inside and has different radii of inner and outer circles is a hollow cylinder.
If Ri is the internal radius and Ro is the outer radius and h is the height of the hollow cylinder then:
- Base surface area = Π (Ro2 – Ri2)
- Curved surface area = 2πRih (Ro + Ri)
- Total surface area = 2π (Ro + Ri) ( h + Ro – Ri)
- Volume = π (Ro2 – Ri2) h
Exercise Discussions of RD Sharma Solutions for Class 9, Chapter 19: Surface Area and Volume of a Right Circular Cylinder
- The first exercise of this chapter of RD Sharma Class 9 Maths Solutions has 14 questions where you need to apply formulas for curved surface area and total surface area of a right circular cylinder to find out their values given radius or height. Most of the problems are short answer types and there are some word problems too.
- The 2nd exercise has 32 questions where most problems need you to find the volume of a right circular or hollow cylinder. It’s a mix of word problems and straight forward questions where you just need to replace the values in formulas.
- The 3rd exercise with 4 questions is VSAQs or very short answer questions. They are simple questions where few definitions and formulas are asked along with 2 sums on finding the volume of a right circular cylinder.
- The 4th exercise is MCQ and has 20 questions. Thes questions require you to apply all the theorems for right circular or hollow cylinder-like curved surface area, volume, number of surfaces, and total surface area.
Benefits of RD Sharma Solutions for Class 9, Chapter 19: Surface Area and Volume of a Right Circular Cylinder
We have a team that has in-depth knowledge of mathematics and they understand your needs as well. That is why when you take help from our solutions, you will find it much easier to cope with the stressful exam environment and manage your time better.
We have provided you with many tips and shortcut methods that will come handy while solving these surface area problems.
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