Unit-2. Properties of Matter. Solutions 2.2 Solids page V sphere. =V cylinder. π.r 2.h= 4 3.π.r 3. h= 4r 3 =4.6 =8 cm

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1 page - 74 V sphere =V cylinder 1. The radius of a sphere and a cylinder are 6 cm. If their volumes are the same, what is the SA/V ratio of the cylinder? π.r 2.h= 4 3.π.r 3 h= 4r 3 =4.6 =8 cm 3 SA V =2 r +2 h = = 7 12 cm-1

2 page Suppose you have two solid cubes made from the same material. The big cube has a mass of 8 kg, while the small one has a mass of 1 kg. a) If the big cube is 10 cm along one side, what is the length of one side of the smaller cube? a) m big m small =8 V big V small =8 V big = a 3 big V small a 3 small =8 a big a small =2 a big =10 cm a small =5 cm b) If the surface area of the small cube is A, what is the surface area of the big cube, in terms of A? b) a big =2 SA big = a 2 big a small SA small a 2 small SA small =A SA big =4A =4

3 page A student peels a big and a small apple. The big apple has 40 cm 2 skins and the small one has 10 cm 2 skins. Suppose that the apples are nearly spherical. How many times is the radius of the big apple greater than that of small apple? Skin Surface Area (SA) SA big SA small = =4 SA big = r 2 big SA small r 2 small =4 r big r small =2

4 page - 74 for sphere for cube 4. The surface area-to-volume ratio of a sphere is equal to the surface area-to-volume ratio of a cube. (π=3) Calculate the ratio of the volumes of the sphere and the cube. SA = V 3 r 3 r SA 6 = V a 6 = a a= 4.3.r 3 V s 3 = = 4.r3 = 1 V c a 3 8.r 3 2

5 page Cylinders X, Y and Z are all made of the same material.! D= Strength $ # & " Weight % cylinder = CSA V =1 h r r X Y Z Compare their strengths per their weight. D X = 1 ' ) D Y = 1 ) ( D X =D Z <D Y r ) D Z = 1 ) ) *

6 page - 75 m initial m final = 1 8 V initial V final = One side of a cube is a and its strength per its weight is D. (Suppose that the density of the cube remains constant.) How would a and D change when the mass of the cube is increased by 8 times? V initial = a3 = 1 V final a 3 final 8 a final=2a D= CSA V =1 a D initial = 1 a D final= 1 2a D initial =D D final = D 2

7 page Ropes A and B are made of the same material. The radius of cross-section of rope A is r and it can barely carry a load of weight G. Strength of the rope is directly proportional to the cross-sectional area of the rope. To carry the weight G, the cross-sectional area is A To carry the weight 3G, the cross-sectional area must be 3A What must be the radius (r / ) of rope B to carry the load of 3G? Cross-sectional area is directly proportional to the square of the radius. r = 3 r

8 page Answer the following question. a) What happens to the strength per body weight of an animal, as it gets larger? decreases Because the strength per body weight is inversely proportional to the linear dimension. b) When the edges of a cube increase by 3 times, how many times does its surface area increase? 9 times Because the surface area is directly proportional to the square of linear dimension. c) When the edges of a cube increase by 10 times, how many times does its volume increase? 1000 times Because the volume is directly proportional to cube of the linear dimension. d) When the mass of a sphere increases by 64 times, how many times does its radius increase? 4 times Because mass is directly proportional to volume. Volume is directly proportional to the cube of linear dimension.