Question

Please answer the following questions :-

1. Find the probability of obtaining two heads on tossing two coins.

2. Simplify
(4a2 +32 a +64 ) ÷ 4

3. Find the total surface area and the lateral surface area of a cube whose side is 0.7 m.

4. A Concrete pillar is in the shape of a cylinder with a radius of 20 cm and a height of 2m, find the volume of the pillar.

5. What is the probability that the number selected from 1,2,3,………..,10 is a composite
number ?

6. The volume of a cuboid is 528 cu.cm and the area of its base is 88 sq.cm. Find its height.

7. Three cubes whose edges are 6cm, 8cm, and 10cm respectively are melted without any loss of metal into a single cube. Find the edge of a new cube.

8. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3 . Find the ratio of their volumes.

9. The weights of 20 students are as follows.
55 ,60 ,65,53,52,51,45,63,49,66,50,48,62,60,57,61,48,51,55,53. Find the range of the
observations and make a frequency distribution table with the class interval 5.

10.How many bricks of dimension 20cm x 10cm x 8cm are required to construct a wall 3m long, 2m wide and rock thick.

11. Prepare a histogram for the following data with class interval 5152,153,144,141,157,161,142,154,155,147,162,148,150,145,154,163,160,143,158,155.

Answer 1

Example 1: Find the surface area if the length of one side is 1/2 cm. 
Solution: 
SA = 6 × a2 
SA = 6 × (1/2)2 
SA = 6 × 1/2 × 1/2 
SA = 6 × 1/4 
SA = 1.5 cm2 


Example 2: Find the Surface area of a cube of side length 8 cm.
Solution: 
SA = 6 × a2
SA = 6 × (8)2
SA = 6 × (64)
SA = 384 cm2


Example 3: Find the total surface area of a box whose edges are all 4.5 cm long.
Solution: 


SA = 6 × l2
SA = 6 × 4.52
SA = 121.5


Example 4: A 5 cubic centimeter cube is painted on all its side. If it is sliced into smaller cubes, that each has a volume of 1 cubic centimeter, how many smaller cubes will have exactly one of their sides painted?
Solution: 
When a 5 cc (cubic centimeter) cube is sliced into 1 cc cubes, we will get 5*5*5 = 125 1 cc cubes. In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted. Therefore, the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted.

In each face of the larger cube, there will be 5*5 = 25 cubes. Of these, there will be 16 cubes on the edge and 3*3 = 9 cubes which are not on the edge. Therefore, there will be 9 × 1 cc cubes per face that will have exactly one of their sides painted.

In total, there will be 9*6 = 54 such cubes.


Example 5: A cube of length 4 cm is cut into smaller cubes with 1 cm in length. What is the percentage increase in the surface area after such cutting?
Solution: 
The volume of the big cube:
V = a3
V = 43
V = 64 cc

When it is cut into 1 cm cube, the volume of each of the cubes = 1cc. Hence, there will be 64 such cubes. 

The surface area of the smaller cubes = 6 (12) = 6 cm2.

Therefore, the surface area of 64 such cubes = 64 * 6 = 384 cm2.
The surface area of the big (original) cube = 6(42) = 6*16 = 96 cm2.


% increase = (384 – 96) / 96 × 100 = 300%
Example 6: A cube whose sides are 10.7 cm in length. Find the surface area of the cube.
Solution:
Given that:
Side length (a) = 10.7 cm
Surface area of the cube:
SA = 6 a2
SA = 6 × (10.7)2
SA = 686.94 cm2

Example 7: Find the surface area of a cube whose side is 1/6 cm.
Solution: 
Given that:
Length of side is 6 cm or a = 1/6

Surface area of the cube:
SA = 6 a2
SA = 6 × (1/6)2
SA = 1/6 cm2

Answer 2

Hope it helps you.......