- PDF Free Download

Size: px

Start display at page:

Download ""

Elwin Snow
5 years ago
Views:

1 FORMULAE: VOLUMES & SURFACE AREA 1. Cuboid Let, length = l, breadth = b and height = h units. (i) Volume of Cuboid = (l b h) cubic units. (ii) Whole surface of cuboid = (lb + bh + lh) sq.units. (iii) Diagonal of cuboid = units.. Cube Let each edge (or side) of a cube be a units, then (i) Volume of Cube = a cubic units. (ii) Whole surface of cube = 6a sq.units. (iii) Diagonal of cuboid = units.. Cylinder Let the radius of the base of a cylinder be r units and its height (or length) be h units, then (i) Volume of the cylinder = (πr h) cubic units. (ii) Curved surface area of the cylinder = (πrh) sq. units (iii) Total surface area of the cylinder = (πrh + πr h) sq.units. 4. Sphere Let the radius of a sphere be r units, then (i) Volume of the sphere = (ii) Surafce area of the sphere = (4πr ) sq. units. (iii) Volume of a hemisphere = l + b + h ( a ) 4 πr πr cubic units. (iv) Curved surface area of the hemisphere = (πr ) square units. (v) Whole surface area of the hemisphere = (πr + πr ) = (πr ) square units. 5. Cone Let r be the radius of the base, h the height and l the slant height of a cone, then (i) Slant height l = h + r

2 (ii) Volume of the cone = 1 π rh cu. units. (iii) Curved surface area of the cone = (πrl) sq. units = PROBLEMS 1. The surface area of a cube is 84 cm. Its volume is? Ans: 1) 55 cm ) 65 cm ) 51 cm 1) 51 cm Sol: 6a = 84 a = 64 a = 8... Volume = (8 8 8) cm = 51 cm. The diagnal of a cube is 4 m. Its volume is? Ans: 1) 86 m ) 89 m ) 100 m 4) 96 m Sol: Let the edge of the cube be a metres Then a = 4 or a = 4... Edge = 4 m So, volume = (4 4 4)m =96 m sq. units. What is the length of the longest pole that can be placed in a room 5 m long, 4 m broad Ans: 1 and m high. 1) 7.05 m ) 7.50 m ) 7.00 m 4) 7.07 m Sol: Length of longest pole = Length of diagonal. = m ( π r r ) + h = 50 m = 5 m = (5 1.41) m = 7.05 m

3 4. What is the volume, surface area and the length of diagonal of a cuboid 1 m long, 9 m broad and 8 m high? 1) 15 m ) 17 m ) 16 m 4) 18 m Ans: Sol: Volume = (1 9 8)m = 864 m Surface area = ( ) m = 55 m Diagonal = = 89 m = 17 m. 5. Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube. What is the length of Ans: 4 the edge of the new cube. 1) 7 cm ) 18 cm ) 6 cm 4) 9 cm Sol: Volume of new cube = = 79cm... Edge of new cube = = 9 cm 6. The capacity of a cylindrical tank is 6160 m. If the radius of its base is 14 m, what is Ans: the depth of the tank? cm 1) 9 m ) 10 m ) 1 m 4)16 m Sol: 14 h = ( ) ( ) ( ) () 6 + () 8 + () 1 ( ) h = 6160 = 10 m The volume of a sphere is 8808 cu. cm. The curved surface area of the sphere is? 1) 5544 sq. cm ) 186 sq. cm ) 816 sq. cm 4) 4158 sq. cm Ans: 1 4 Sol: Given the volume of the sphere: πr = 8808

4 r 7 = 8808 = (1) 4 r = 1 cm So, the curved area of sphere = 4πr = cm 7 = 5544 cm 8. The length of cylinder is 80 cm and the diameter of its base is 7 cm. The whole surface Ans: 1 of the cylinder is? 1) 187 cm ) 1760 cm ) 080 cm 4) 194 cm Sol: Given diameter = 7 cm, so radius r =.5 cm And h = 80 cm. Whole surface = (πrh + πr h) = πr(h + r) =.5 (80 +.5) cm 7 = 8.5 = 187 cm 9. If the volumes of two cones are in the ratio 1:4 and their diameters are in the ratio 4:5, Ans: 4 then the ratio of their heights is? 1) 1:5 ) 5:4 ) 5:16 4) 5:64 Sol: Since the diameters are in the ratio 4:5. It follows that their radii are in the ratio 4:5. Let them be 4r and 5r. Let the heights be h and H 1 π ( 4r) h 16h 16h Ratio of volumes = = = 1 5H 5H π ( 5r) H 1 4 h : H = 5: 64

5 10. If a right circular cone of vertical height 4 cm has a volume of 1 cm, then the area of its curved surface is? 1) 154 cm ) 704 cm ) 550 cm 4) 154 cm Ans: Sol: Given volume of the cone is 1 cm 1 7 Now, = 1 r 7 = 1 = 49 4 r = 7 cm. and h = 4 l = = 65 = 5 cm Curved surface area = πrl = 7 5 cm = 550 cm 7 EXERCISE 1. A wooden box of dimensions 8 m 7 m 6 m is to carry rectangular boxes of dimensions 8 cm 7 cm 6 cm. The maximum number of boxes that can be carried in 1 wooden box is? r 4 1) ) ) ) The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is cm. Its surface area is? 7 + (4) 1) 61 cm ) 15 cm ) 6 cm 4) 486 cm 5 5. If the length of diagonal of a cube is 8 cm, then its surface area is? 1) 51 cm ) 84 cm ) 19 cm 4) 768 cm

6 4. The length of longest rod that can be placed in a room 0 m long, 16 m broad and 1 m high, is? 1) 0 m ) 16.4 m ) 48 m 4) 8. m 5. If each side of a cube is doubled, then its volume is? 1) Is doubled ) Becomes 4 times ) Becomes 6 times 4) Becomes 8 times 6. The curved surface area of a sphere is 186 sq. cm. Its volume is? 1) 77 cm ) 4158 cm ) 4851 cm 4) 5544 cm 7. The radius of a circular cylinder is the same as that of sphere. Their volumes are equal. The height of the cylinder is? 4 1) times its radius ) times its radius ) Equal to its radius 4) Equal to its diameter 8. The length of the wire of 0. mm readius that can be drawn after melting a solid copper sphere of diameter 18 cm, is? 1) 4. m ) 4 m ) 40 m 4) 400 m 9. The radius of two cylinders are in the ratio of : and their heights are in the ratio 5:. The ratio of their volumes is? 1) 7:0 ) 0:7 ) 4:9 4) 9:4 10. If the radius of a sphere is doubled, then its volume is increased by? 1) 100% ) 00% ) 700% 4) 800% 11. The area of the base of a right circular cone is 154 cm and its height is 14 cm. The curved surface of the cone is? ( ) ( ) 1) cm ) 11 cm ) cm 4) 54 cm

7 10. The material of a cone is converted into the sphere of a cylinder of equal radius. If the height of the cylinder is 5 cm, the height of the cone is? 1) 10 cm ) 15 cm ) 18 cm 4) 4 cm ANSWERS

SURFACE AREAS AND VOLUMES

CHAPTER 1 SURFACE AREAS AND VOLUMES (A) Main Concepts and Results Cuboid whose length l, breadth b and height h (a) Volume of cuboid lbh (b) Total surface area of cuboid 2 ( lb + bh + hl ) (c) Lateral