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In this chapter, we will study these in details. Archimedes of Syracuse, Sicily, is remembered as the greatest Greek mathematician of the ancient era. He contributed significantly in geometry regarding the areas of plane figures and the areas and volumes of solid figures. He proved that the volume of a sphere is equal to two-third the volume of a circumscribed cylinder. Download and practice to score good marks and solve your doubts easily. A metallic sphere of radius 4. Find the height of the cylinder.
Water in a canal, 6 m wide and 1. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed? A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius.
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. Assume the outer and inner dimensions of the model to be nearly the same. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.
A pen stand made of wood is in the shape Ncert Solutions Class 10th Maths Chapter 2 Github of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3. The radius of each of the depressions is 0. The volume of solids by joining two or more basic solids is the sum of the volumes of individual solids.
Let us understand this with an example:. The solid in the above figure is made up of two solids, i. So the total volume of the solid is obtained by adding up the volume of these two constituent solids. When we convert a solid from one form to another by the method of melting or remoulding, then the volume of the solid stays the same, despite the change in shape. We will see an example to understand why:.
Solution - From the theorem on volumes, we know that volume of the water in the cylinder and the volume of the water in the cuboid would be the same. If the water fills the cylinder to the brim then:. Many students often find it difficult to remember important Mathematical formulas and even in solving textbook exercises.
They can list down these formulas and revise them on a regular basis. Doing this will help students solve the exercises more efficiently. These solutions are solved in a very simple and step-by-step manner to help the students to understand and solve the problems easily.
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