BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPÉCIFIQUE MENTION « SECTION EUROPÉENNE OU DE LANGUE ORIENTALE »
Académies de Paris-Créteil-Versailles
Binôme : Anglais / Mathématiques Sujet 3 VOLUMES The first part of this page is a summary that can help you to do the exercise.
The general formula for the volume V of a prism or a cylinder is V = (area of the cross-section) × length. Notice that a cuboid is a prism whose six faces are all rectangles : then the area of its cross-section is that of a rectangle. In case of a cylinder, the cross-section is a circle, whose area is πr2 if r is its radius. The general formula for the volume V of a pyramid or a cone is V = 1 (base area) × height 3 3 4 The volume of a sphere is π r where r is the radius of the sphere. 3 Volumes of similar objects: When solid objects are similar, one is an accurate enlargement of the other. If two objects are similar, and the ratio of corresponding sides is k, then the ratio of their volumes is k3. EXERCISE: Morph made several different objects from modelling clay. He used 500 cm3 of clay for each object. (a) He made a square-based cuboid of height 2 cm. Calculate the length of a side of the square. (b) He made a pyramid with a base area of 150 cm2. Calculate the height of the pyramid. (c) He made a sphere. Calculate the radius of the sphere, correct to 1 d.p.. (d) He wrapped the clay around the curved surface of a hollow cylinder of height 6 cm. The thickness of the clay was 1.5 cm. Calculate the radius of the hollow cylinder, correct to 1 d.p..
(e) He made a cone. Then he cut through the cone, parallel to its base, to obtain a small cone and a frustum. The height of the small cone was two-fifths of the height of the full cone. Use a property of the volumes of similar objects to calculate the volume of clay in the small cone.
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