Amandeep went to a painter to get he solid object in the shape of a cylinder with hemispherical ends to be painted The whole length of the solid was 108 cm and diameter of the hemispherical ends was 36 cm. Painter calculated the cost of painting as 558 (approx.) at the rate of 5 paisa per sq. am but Amandeep calculated the correct amount and paid this amount to the painter ( What was the correct amount which Amandeep had paid ? (I) Find the difference in amount.
Answers
The correct amount which Amandeep had paid was Rs. 610.97 and the difference in the amount is Rs. 52.97 .
Step-by-step explanation:
Step 1:
The object that Amandeep has is in the shape of a cylinder with hemispherical ends.
The total length of the object = 108 cm
The diameter of the hemispherical ends = 36 cm
∴ The radius of the hemispherical ends = diameter/2 = 36/2 = 18 cm
∴ The height of the cylinder will be = 108 – (18+18) = 72 cm
Now,
The total surface area of the solid object is given by,
= [CSA of the cylinder] + [CSA of the 2 hemispherical ends]
= 2πrh + 2 *[2πr²]
= 2πr [h + 2r]
= 2 * 22/7 * 18 * [72 + (2*18)]
= 2 * 22/7 * 18 * 108
= 12219.42 cm²
Step 2:
The rate of painting the solid is 5 paisa or Rs. 0.05 per sq. cm
Therefore,
The total cost of painting the solid object which is the correct amount calculated by Amandeep is given by,
= 12219.42 cm² * Rs. 0.05
= Rs. 610.97
But it is given that the painter had calculated the amount as Rs. 558 (approx.)
Therefore,
The difference in the amount = Rs. 610.97 – Rs. 558 = Rs. 52.97
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