VOLUME & SURFACE AREA OF SPHERE BY MAYANK AGNIHOTRI

SPHERE A sphere is three-dimensional figure which consist of all those points in the space, which are at a constant distance from a fixed point. This fixed point is called the centre of the sphere and the constant distance is called its radius. Example Football, basketball etc Volume of sphere-4 3 . Surface area of sphere = 4 2 where, r-radius of sphere

I HEMISPHERE If we cut a sphere into two equal parts then each of these two equal parts is called hemisphere . Volume of hemisphere=1 3 3=2tr3 Curved surface area of hemisphere = 2 Total surface area of hemisphere = curved surface area of hemisphere + Area of the base of hemisphere 2 where, r = radius of hemisphere

Questions Ques 1. How many balls each of radius 2 cm can be formed by melting a big ball of radius 8 cm? (1) 30 (2) 64 (3) 74 (4) 80 Sol Radius of big ball (R) 8 cm and radius of small ball (r) 2 cm Volume of big ball = 4 R3 = (8)3 cm3 Volume of small ball =- 3-- (2)3 cm" Volume of big ball -3r(8)"-8x8x8- Volume of small ball (2)32x2x2 balls Ans Required number of balls Ques 2. A hemisphere has 3 cm radius. Calculate its curved surface area and Total surface area Sol. Curved surface area = 2 2-2 32-18 cm2 Ans Total surface areas 3 2-3 >< 32-27 cm2 Ans

Ques 3. If the radius of sphere is increased by 50%, then the surface area will increase by how much percent? Sol Let the original radius be = r & the new radius be = r, 50 100 150r 100 Now, Percentage change in surface areas = 4m2-4mr2 4tr2 15rA 100 4Ttr2 4tr2(150)2 100 iTr2(1050-1 150x150-100x100 100 4 ?- 4x 100 = 150X150 100 100 150 150-100 100 22500-10000 100 12500 -12590 Ans 100 100

Ques 4. The volume of two hemispheres are in the ratio 8: 27. What is the ratio of their radii? (1)3:2 (2) 4 9 (3) 2:3 (4) 8:27 Sol Let volume of 1st hemisphere be v & its radius be ri Let volume of 2nd hemisphere be v2 & its radius be r2 its is given that 8 v2 27 tri 8 27 3 8 2 V27 3

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Mayank Agnihotri

B.Tech (ECE), Machine enthusiast, Inspired by an old hindi saying " Gyan baatne se badhta ha"

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Sunanda Suresh

4 months ago

thank you sir

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