If three cylinders of radius r and height h are placed vertically such that the curved surface of each cylinder touches the curved surfaces -Maths 9th

If three cylinders of radius r and height h are placed vertically such that the curved surface of each cylinder touches the curved surfaces -Maths 9th
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Answer :

hr2 (3–√−π2)(3−π2) The bases of the three cylinders when placed as given are as shown in the figure :  Let the radius of the base of each cylinder = r cm.  We are required to find the volume of air.  Space left between the cylinders = Area of shaded portion x height of cylinder  Now, area of shaded portion  = Area of ΔABC – Sum of areas of sectors of the three bases ΔABC, as can be seen is an equilateral triangle of side 2r.  ∴ Area of Δ ABC = 3√4×(2r)2=3–√r234×(2r)2=3r2 Area of (sector AEF + sector BED + sector CFD) (∴ sector angles ∠A = ∠B = ∠C = 60º)  = 3 x 60o360o×πr2=πr2260o360o×πr2=πr22 ∴ Required volume = (3–√r2−π2r2)h=(3–√−π2)r2h.
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Description : The radius of a right circular cone is 3 cm and its height is 4 cm. The curved surface of the cone will be (1) 12 sq. cm (2) 15 sq. cm (3) 18 sq. cm (4) 21 sq. cm

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Last Answer : According to question 4q 2 = p 2+ 3r 2.

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AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre. Prove that -Maths 9th

Description : AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre. Prove that -Maths 9th

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