1. Volume = (l x b x h) cubic units.
2. Surface area = 2(lb + bh + lh) sq. units.
3. Diagonal = √l^2 + b^2 + h^2 units.
3. Diagonal =√ 3a units.
A.1 : 5
B.1 : 25
C.1 : 125
D.1 : 625
2.The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is
3.A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is
4.How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
5.A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
6.A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
7.A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is
8.The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is
9.Five equal cubes, each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be
10.An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are
A.10 cm, 50 cm
B.20 cm, 100 cm
C.40 cm, 200 cm
D.None of these
Answer With Explanations:
1.(6x1x1 / 6x5x5)
‹=› 1/ 25
‹=› 1 : 25.
2.Surface area = (34398 / 13)
‹=›a = 21.
So,volume =(21x21x21)cm^3= 9261cm^3
3.Volume of water displaced = (3 x 2 x 0.01)m^3
Mass of man =Volume of water displaced ×Density of water
= (0.06×1000) kg
= 60 kg.
4.Number of bricks = Volume of the wall/Volume of 1 brick
5. 2(15 + 12) ×h = 2(15 x 12)
‹=›h= 180/27 m
Volume = (15×12×20/3)m^3
6. External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron =(22/7×(42)-(32)×21)cm^3
= (22/7×7 ×1×21)cm^3
= 462 cm^3.
8. 4?R^2= 2?6×12
R^2 = (6×12/2)= 36
R = 6 cm.
9.The new solid formed is a cuboid of length 25 cm, breadth 5 cm and height 5 cm
Volume = (25x5x5)cm^3
10.Let the sides of the sheet be x and 5x.
Then,volume of the sheet= volume of the cube
‹=› x × 5x ×1/2
‹=› 5x^2= 2000
‹=› x^2= 400
‹=› x = 20.
The sides are 20 cm and 100 cm.
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