Question

the outer and inner diameter of hemispherical bowl are 17cm and 15cm. find the cost of polishing it over at 25 paise percm2​

Answer 1

Step-by-step explanation:

• The outer diameter of hemispherical bowl (R) = 17cm
• The inner diameter of hemispherical bowl (r) = 15cm
• The rate of polishing = Rs.25 cm²

The CSA of outer hemispherical bowl = 2πr²

• 2 × 3.14 × (17)²
• 2 × 3.14 × 289
• 1814.92 cm²

The CSA of inner hemispherical bowl = 2πr²

• 2 × 3.14 × (15)²
• 2 × 3.14 × 225
• 1413 cm²

The CSA of ring = 2π ( R - r )²

• 2 × 3.14 × [ (17)² - (15)² ]
• 2 × 3.14 × (289 - 225)
• 401.92 cm²

Total surface area (TSA) = CSA of outer hemispherical bowl + CSA of inner hemispherical bowl + CSA of ring

• TSA = 1814.92 + 1413 + 401.92
• TSA = 3629.84 cm²

:. The cost of polishing 1 cm = Rs. 25 cm²

The cost of CSA of ring (401.92) = ?

• 0.25 × 401.92
• Rs. 100.48 paise per cm²

:. The cost of polishing at 25 paise per cm² is 100 and 48 paise .

Answer 2

Given :-

• Outer diameter of a hemispherical bowl = 17 cm

• Inner diameters of a hemispherical bowl = 15 cm

• The cost of polishing it over at 25 paise/cm².

To Find :-

• The cost of polishing the hemispherical bowl.

Solution :-

To polish the hemispherical bowl we need the inner & outer C.S.A.

Outer diameter of a hemispherical bowl = 17 cm

Outer radius = 17/2

Inner diameters of a hemispherical bowl = 15 cm

Inner radius = 15/2

We know, The T.S.A of hemisphere is 2πr² .

The inner C.S.A of hemisphere = 2πr²

➝ 2 × 22/7 × (17/2 × 17/2)

➝ 2 × 22/7 × (17/2 × 17/2)

➝ 2 × 22/7 × 289/4

➝ 454.142 cm²

The inner C.S.A of hemisphere = 2πr²

➝ 2 × 22/7 × (15/2 × 15/2)

➝ 2 × 22/7 × (15/2 × 15/2)

➝ 2 × 22/7 × 225/4

➝ 343.571 cm²

The CSA of ring = 2π (R - r )²

➝ 2 x 22/7 x {(17)² - (15)²}

➝ 2x22/7 x (289 - 225)

➝ 2x22/7 x 64

➝ 401.92 cm²

Net area to be painted of the bowl = Outer CSA + Inner CSA + area of ring

➝ 454.142 + 343.571 + 401.92

➝ 1199.633 cm²

The cost of polishing it over at 25 paise/cm².

25 paise = 0.25 rupees

➝ 1199.633 × 0.25

➝ 299.908 rupees

The cost of polishing it over at 25 paise/cm is 299.908 rupees .

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