Question

.. A round table cover has six equal designs as shown
in Fig. 12.14. If the radius of the cover is 28 cm, find
the cost of making the designs at the rate of
*0.35 per cm². (Use 13 = 1.7)​

Answer 1

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refer to the attachment.

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Answer 2

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