Cylinder, Cone and Sphere (Surface Area and Volume) Solutions for ICSE Board Class 10 Mathematics (Concise - Selina Publishers)
FAQs on Cylinder, Cone and Sphere Solutions for ICSE Board Class 10 Mathematics
1. What are some important formulae of a cylinder?
We call it a Right Cylinder when the producing line is perpendicular to the base. However, an oblique cylinder is one in which one of the bases appears sideways, i.e. not perpendicular to the base. Let's look at some of the most significant formulas now.
The volume of a cylinder = Area of base × Height of cylinder = πr²h
The Lateral Surface Area (LSA) = Perimeter of base × height = 2πrh = πdh
The Total Surface Area (TSA) = The Lateral Surface Area (LSA) + Area of bases = 2πrh + 2πr² = 2πr (h+r)
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2. What are the formulas of a hollow cylinder?
Another element of cylinders that we need to understand is a hollow cylinder, such as a pipe. The formulas will alter significantly in this case. There are two radii to remember here: R for the outer cylinder and r for the inner cylinder.
The Volume of Hollow Cylinder = The Volume of External Cylinder – The Volume of Internal Cylinder = πR²h – πr²h = π (R² – r²) h
The Lateral Surface (hollow cylinder) = The External Surface Area + The Internal Surface Area = 2πRh + 2πrh = 2π(R+r)h
The Total Surface Area (cylinder) = The Lateral Area = The Area of bases = 2π(R+r)h + 2π (R² – r²) h
3. What are the important formulae of a cone?
A cone is a solid three-dimensional geographic feature with a flat circular (or roughly circular) base that tapers smoothly to the vertex or tip. Therefore, the cone is made by a solid generated by a line with one end fixed and the other describing a closed curve on a plane. Let's have a look at some cone formulas.
Volume of a cone = 13 area of base × height = 13 πr²h
Lateral Surface = 12 radius × arc length = 12 l × 2πr = πrl
where l = slant height = √(r² + h²)
Total Surface Area (TSA) = lateral surface area (LSA) + Area of base = πrl + πr²
4. What are some important formulae of a sphere?
A sphere is a solid round three-dimensional shape with equal distances between all points on its surface. As a result, a sphere's radius is all equal. A football, basketball, or other sphere is the finest example. The hemispheres are formed when a large circle divides the sphere into two equal pieces. Let's have a look at the most important formulas.
The Surface Area of a Sphere (TSA) = 4 times of its great circle = 4πr² = πd²
The Volume of a Sphere = 43 πr² = π6 d³
5. How to prepare the topic of Cylinder, Cone and Sphere of Class 10 Mathematics?
Firstly, students need to learn the basic properties of the cylinder, cone and sphere. They need to possess strong fundamentals about all the three figures, i,e, cylinder, cone and sphere. Then, they need to be thorough with the formulas related to the cylinder, cone and sphere. It would be a huge advantage for the students if they can learn how the formulas are derived. As that would cement the formulas more firmly in their mind. Finally, practice is very important for students to ace the exams. Students can always try to solve the sample papers related to the exam. Students can check out the Vedantu app and website which has free study materials.