Math, asked by chandniprabhu7, 4 months ago


A round table cover has six equal designs as shown in figure. If the radius of the cover is 56 cm, find
the cost of making the design at the rate of 3.5 per cm2. (Use root 3=1.7, pie(ll), =22/7​

Answers

Answered by Anonymous
1

Answer:

here is your answer mate

Step-by-step explanation:

r=28cm,θ=  

6

360  

0

 

​  

=60  

0

 

Area OAMB=  

360  

0

 

θ

​  

×πr  

2

=  

360  

0

 

60  

0

 

​  

×  

7

22

​  

×28×28

                        =  

3

1232

​  

cm  

2

=410.67cm  

2

 

Now,  in ΔONA and ΔONB

      i)  ∠ONA=∠ONB[each90  

0

]

     ii)  OA=OB    [Radii of common circle]

    iii)  ON=ON    [common]

∴ΔONA≅ΔONB[ByRHScongruency]

Hence, AN=NB=  

2

1

​  

AB

&   ∠AON=∠BON=  

2

1

​  

∠AOB=  

2

60  

0

 

​  

=30  

0

 

Now in ΔONA,cos30  

0

=  

OA

ON

​  

⇒  

2

3

​  

 

​  

=  

28

ON

​  

⇒ON=14  

3

​  

cm

& sin30  

0

=  

OA

AN

​  

⇒  

2

1

​  

=  

28

AN

​  

⇒AN=14cm

&  2AN=14×2=28cm=AB

∴ arΔAOB=  

2

1

​  

×AB×ON=  

2

1

​  

×28×14  

3

​  

=196  

3

​  

=196×1.7 =333.2cm  

2

 

∴ Area of one design =410.67−333.2=77.47 cm  

2

 

∴ Area of six design= 6×77.47=464.82cm  

2

 

Therefore, Cost of making the designs=Rs.(464.82×3.5$$)

                                                                =Rs.1626.8

please mark me as a brainlist

Answered by 2602alpha
1

Answer:

r=28cm,θ=  

6

360  

0

 

​  

=60  

0

 

Area OAMB=  

360  

0

 

θ

​  

×πr  

2

=  

360  

0

 

60  

0

 

​  

×  

7

22

​  

×28×28

                        =  

3

1232

​  

cm  

2

=410.67cm  

2

 

Now,  in ΔONA and ΔONB

      i)  ∠ONA=∠ONB[each90  

0

]

     ii)  OA=OB    [Radii of common circle]

    iii)  ON=ON    [common]

∴ΔONA≅ΔONB[ByRHScongruency]

Hence, AN=NB=  

2

1

​  

AB

&   ∠AON=∠BON=  

2

1

​  

∠AOB=  

2

60  

0

 

​  

=30  

0

 

Now in ΔONA,cos30  

0

=  

OA

ON

​  

⇒  

2

3

​  

 

​  

=  

28

ON

​  

⇒ON=14  

3

​  

cm

& sin30  

0

=  

OA

AN

​  

⇒  

2

1

​  

=  

28

AN

​  

⇒AN=14cm

&  2AN=14×2=28cm=AB

∴ arΔAOB=  

2

1

​  

×AB×ON=  

2

1

​  

×28×14  

3

​  

=196  

3

​  

=196×1.7 =333.2cm  

2

 

∴ Area of one design =410.67−333.2=77.47 cm  

2

 

∴ Area of six design= 6×77.47=464.82cm  

2

 

Therefore, Cost of making the designs=Rs.(464.82×3.5$$)

                                                                =Rs.1626.8

Similar questions