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Nastasia [14]
2 years ago
13

From a circular cylinder of diameter 10 cm and height 12 cm are conical cavity of the same base radius and of the same height is

hollowed out. Find the volume and the whole surface of the remaining solid.
(take \ \: \pi \:  = 3.14)


​
Mathematics
1 answer:
Nataliya [291]2 years ago
6 0
<h3>Volume of the remaining solid = 628 cm^2</h3>

<h3>Whole surface area = 659.4 cm^2</h3>

Step-by-step explanation:

Now, Given that:-

Diameter (d) = 10 cm

So, Radius (r) = 10/2 = 5cm

Height of the cylinder = 12cm.

volume \: of \: the \: cylinder \:  =  \pi {r}^{2} h

=  > \pi \times  {5}^{2} \times  12 {cm}^{3}   = 300\pi {cm}^{3}

Radius of the cone = 5 cm.

Height of the cone = 12 cm.

slant \: height \: of \: the \: cone \:  =  \sqrt{ {h}^{2}  + \:  {r}^{2} }

=  >  \sqrt{ {5}^{2}+{12}^{2} } cm \:  = 13cm

Volume of the cone = 1/3 *πr^2h

=  >  \frac{1}{3} \pi \times  {5}^{2}   \times 12 {cm}^{3}  = 100\pi {cm}^{3}

therefore, the volume of the remaining solid

= 300\pi {cm}^{3}  - 100\pi {cm}^{3}  \\  = 200 \times 3.14 {cm}^{3}  = 628 {cm}^{3}

Curved surface of the cylinder =

2\pi \: rh \:  = 2\pi \times 5 \times 12 {cm}^{2}  \\  = 120\pi {cm}^{2} .

curved \: surface \: of \: the \: cone \:  = \pi \: rl \\  = \pi \times 5 \times 13 {cm}^{2}  \\  = 65\pi {cm }^{2} \\ area \: of \: (upper)circular \: base \: \\  of \: cylinder \:  =  \\ =  \pi \:  {r}^{2}  = \pi \times  {5}^{2}

therefore, The whole surface area of the remaining solid

= curved surface area of cylinder + curved surface area of cone + area of (upper) circular base of cylinder

= 120\pi {cm}^{2}  + 65\pi {cm }^{2}  + 25 \pi {cm}^{2}  \\  = 210 \times 3.14 {cm}^{2}  = 659.4 {cm}^{2}

<h3>Hope it helps you!!</h3>

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Answer:

  -25            

 ——— = -2.08333

    12  

Step-by-step explanation:

Step  1  :

           7

Simplify   —

           4

Equation at the end of step  1  :

       1           7

 (0 -  —) +  (0 -  —)

       3           4

Step  2  :

           1

Simplify   —

           3

Equation at the end of step  2  :

       1     -7

 (0 -  —) +  ——

       3     4

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       3

     The right denominator is :       4

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

3 1 0 1

2 0 2 2

Product of all

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     Least Common Multiple:

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Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

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  Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

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To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      -1 • 4

  ——————————————————  =   ——————

        L.C.M               12  

  R. Mult. • R. Num.      -7 • 3

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Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

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Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

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      12            12

Final result :

 -25            

 ——— = -2.08333

 12            

Processing ends successfully

plz mark me as brainliest :)

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