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Q.

A hemispherical bowl is to be painted from inside at the rate of Rs. 20 per 100 m2. The total cost of the painting is Rs. 30.80. Find the volume of air inside the bowl.

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a

    276.10 m3

b

    355.12 m3

c

    255.17 m3

d

 554.05 m3 

answer is C.

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Detailed Solution

The volume of the bowl = 2 𝜋𝑟3
3
The area painted is 100 m2
The area painted for 1 Rs = 100
20
= 5 m2
Now, we will calculate the area painted for 30.80 i.e 5 × 30.80 = 154 m2
Therefore, the inner surface area of the bowl is 154 m2 The inner surface area of the bowl = 2𝜋𝑟2
⇒ 2 𝜋𝑟2= 154
⇒ 154 = 22 × 22 × 𝑟2
7
 ⇒ r2 = 154 × 7  × 1
22 2
 ⇒ r2 = 49
Question Image2
⇒ r = √49
2
⇒ r = 7
√2
⇒ r = 7 1.414
⇒ r = 4.95
Now, we will find the volume of the bowl The volume of the bowl = 2 𝜋𝑟3
3
= 2 × 7 × 4.95 × 4.95 × 4.95
3 22
= 255.17 m3
  
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A hemispherical bowl is to be painted from inside at the rate of Rs. 20 per 100 m2. The total cost of the painting is Rs. 30.80. Find the volume of air inside the bowl.