From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the total surface area of the remaining solid.​

Answer:

(i). Median Age= 58yrs

(ii). Value of x is 5.85 (approx. 6)

Step-by-step explanation:

Concept= Median and Mean of Grouped data

Given= Distribution Table and Mean

To find= Median and variable x

Explanation=

First we organize the data in our tabular form

Age Group    No. of people([tex]f_{i}[/tex])    C.F            Group Mark([tex]x_{i}[/tex])       [tex]f_{i} x_{i}[/tex]

15-25                   8                          8                           20             160

25-35                  10                         18                          30             180

35-45                  15                          33                          40            600

45-55                  25                         58                          50            1250

55-65                  40                         98                          60             2400

65-75                  24                          122                          70            1680

75-85                  18                            140                          80           1440

                         ∑[tex]f_{i}[/tex]=140                                                                   ∑[tex]f_{i} x_{i[/tex]=7710

(i). Median Age group of people enrolled in camps-

  n=140(cf) , n/2= 70

Thus this observation lies between the age group 55-65(median class).

Lower Class limit(l)= 55, Class size(h)= 10, Frequency of median class(f)= 40

Cumulative frequency of class preceding the median class is(c) 58.

Formula to find median of grouped data is Median= [tex]l+{(n/2-c)/f} * h[/tex]

equating values we get,  Median= 55+(70-58)/40  * 10= 55 +0.3*10= 55+3=58.  

Median Age= 58yrs

(ii). Find x, when x people were added in group 65-75 and Mean was 58.

If x people were  added in that group then number of people will become 24+x , Similarly the [tex]f_{i} x_{i}[/tex] value of 65-75 will become 1680+70x.

So now the new ∑[tex]f_{i} x_{i}[/tex]= 7710+70x .

Mean=∑[tex]f_{i} x_{i}[/tex]/∑[tex]f_{i}[/tex] , Equating the values we have ,

58= 7710+70x/140

=>8120=7710+70x

=>410=70x

=> x= 5.85 (approx. 6)

Therefor value of x is 5.85 (approx. 6)

Answer:

Volume of cone =

3

2

Volume of hemisphere

3

1

πr

2

h=

3

2

(

3

2

πr

3

) ; r =Common radius h = Cone height

h=

3

4

r=

3

4

(21)=28cm

Slant height, l=

r

2

+h

2

=

21

2

+28

2

=35cm

Total surface area = CSA

cone

+CSA

hemisphere

=πrl+2πr

2

=πr(l+2r)=5082cm

2

Solve any question of Surface Areas and

Answer:

(a) volume of 50 toys is 16.155 m³

(b)  [tex]\frac{volume \ of \ hemisphere}{volume \ of \ cone} = \frac{19386.36}{12924.24}[/tex]

Step-by-step explanation:

Given, cone: radius = 21 cm and height = 28 cm

hemisphere: radius = 21 cm

(a) [tex]volume \ of \ hemisphere = \frac{2}{3} \pi\ r^{3}[/tex]

             = [tex]\frac{2}{3} (3.14)(21^{3})[/tex]

             = 19386.36 cm³

  [tex]volume \ of \ cone \ =\frac{1}{3} \pi\ r^{2} h[/tex]

              = [tex]\frac{1}{3}(3.14)21^{2}(28)[/tex]

              =   12924.24 cm³

volume of one toy = 19386.36 + 12924.24

                               =  32310.6 cm³ = 0.3231 m³

volume of 50 toys = 0.3231× 50 = 16.155 m³

(b)  [tex]\frac{volume \ of \ hemisphere}{volume \ of \ cone} = \frac{19386.36}{12924.24}[/tex]

1) ANSWER:- A computer consists of five functionally independent main parts input, memory, arithmetic logic unit (ALU), output and control unit.

2) ANSWER:- Input devices –Mouse, Keyboard, Touchpad, Scanners, Joystick, Webcam, etc. Output devices – Monitor, Printer, Headphones, Speakers, etc. Storage devices – Hard disk, DVD, etc. Internal components – Motherboard, CPU, RAM, etc.

3) ANSWER:-Essentially, information is the result of analyzing and interpreting pieces of data. Whereas data is the individual figures, numbers, or graphs, information is the perception of those pieces of knowledge. For example, a set of data could include temperature readings in a location over several years.

4) ANSWER;-In computing, an input device is a piece of equipment used to provide data and control signals to an information processing system, such as a computer or information appliance. Examples of input devices include keyboards, mouse, scanners, cameras, joysticks, and microphones.

5) ANSWER;-Any peripheral that accepts data from a computer and prints, projects, or reproduces it is known as an output device. The output may be audio, video, hard copy – printed paper, etc. Output devices convert the computer data to human understandable form.

The quadratic equation in terms of x is 4x²-38x+48 = 0 and the width of the sidewalk is 1.5 m.

Given,

The outer edges of the swimming pool are 7m and 12 m.

The width of the sidewalk is x m.

The area of the pool = 36 sq. m

To Find,

The quadratic equation in terms of x, and the width of the sidewalk.

Solution,

Since the width of the sidewalk is x m.

So the dimensions of the pool will be (7-2x) and (12-2x).

Now,

Area of the pool = 36 sq. m

(7-2x)(12-2x) = 36

84-14x-24x+4x² = 36

4x²-38x+48 = 0

4(x-8)(x-3/2) = 0

x = 8, 1.5

The value of x can't be 8 as it will make the dimensions of the pool negative

So, the value of x is 1.5 m.

Hence, the quadratic equation in terms of x is 4x²-38x+48 = 0 and the width of the sidewalk is 1.5 m.

Answer:

The quadratic equation in 'x' is  [tex]2x^2 - 19x +24 = 0[/tex]

Width of the sidewalk = 1.5m

Explanation:

Given,

Area of the pool = 36sq.m.

width of the sidewalk = 'x'm

Length of the pool including the sidewalk = 7m

Breadth of the pool including the sidewalk = 12m

Required to find,

1. Quadratic equation in terms of 'x'
2. Width of the sidewalk

Formula to be used

Area of the rectangle = length x breadth

Length of the pool = 7 -2x

Breadth of the pool = 12 -2x

Area of the pool = (7-2x)(12-2x)

(7-2x)(12-2x) = 36

[tex]84 - 24x - 14x + 4x^2 = 36\\[/tex]

[tex]4x^2 - 38x +48 = 0\\[/tex]

[tex]2x^2 - 19x +24 = 0[/tex]

Hence,

The quadratic equation in 'x' is  [tex]2x^2 - 19x +24 = 0[/tex]

To find 'x'

To solve the quadratic equation by splitting the middle term, we need to find two numbers such that their sum = -19 and product = 48

Two such numbers are = -16 and -3

[tex]2x^2 - 16x - 3x +24 = 0[/tex]

2x (x-8) - 3(x-8) = 0

(2x-3)(x-8) = 0

2x -3 = 0 or x = 8

x = [tex]\frac{3}{2}[/tex] = 1.5 or x = 8

x = 8, is not possible because the length of the pool including the sidewalk is 7m.

So x = 1.5m

Hence,

Width of the sidewalk = 1.5m