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Infographics: Mensuration: Volume, Surface Area & Solid Figures
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FAQs on Infographics: Mensuration: Volume, Surface Area & Solid Figures
| 1. What are the formulas for calculating the volume of common solid figures? |  |
Ans. The volume formulas for common solid figures are as follows: for a cube, the volume is given by V = a³, where 'a' is the length of a side. For a rectangular prism, V = l × b × h, where 'l' is length, 'b' is breadth, and 'h' is height. For a cylinder, V = πr²h, where 'r' is the radius and 'h' is the height. For a sphere, V = (4/3)πr³, and for a cone, V = (1/3)πr²h.
| 2. How do you calculate the surface area of a sphere? | |
Ans. The surface area of a sphere is calculated using the formula A = 4πr², where 'r' is the radius of the sphere. This formula represents the total area that covers the outer surface of the sphere.
| 3. What is the difference between lateral surface area and total surface area? | |
Ans. Lateral surface area refers to the area of the sides of a solid figure, excluding the base or bases. For example, the lateral surface area of a cylinder is given by A = 2πrh, where 'r' is the radius and 'h' is the height. Total surface area, on the other hand, includes the lateral surface area plus the area of the bases. For the same cylinder, the total surface area would be A = 2πrh + 2πr².
| 4. How is the volume of a cone derived? | |
Ans. The volume of a cone is derived from the volume of a cylinder. Since a cone can be thought of as a pyramid with a circular base, its volume is one-third that of a cylinder with the same base and height. Hence, the formula for the volume of a cone is V = (1/3)πr²h, where 'r' is the radius of the base and 'h' is the height.
| 5. Can you explain how to approach mensuration problems in exams like SSC CGL? | |
Ans. To approach mensuration problems in exams like SSC CGL, first, carefully read the question to understand what is being asked. Identify the solid figure involved and recall the relevant formulas for volume and surface area. It is helpful to sketch the figure if necessary. Substitute the given values into the formula and perform the calculations step-by-step, ensuring accuracy. Finally, check your answer against the options provided, if applicable, to confirm correctness.
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