A closed cylindrical brick tank has a diameter of 35 metres and height of 8 metres. What is the volume of the tank? How much will it cost to paint'the curved surface and the top of the tank, if the rate is 5.00 per m??
Answers
{Some corrections in question}
Correct question : A closed cylindrical brick tank has a diameter of 35 metres and height of 8 metres. What is the volume of the tank? How much will it cost to paint the curved surface and the top of the tank, if the rate is Rs 5.00 per m²
Given data :
➜ Diameter of tank, r = 35 m
➜ Height of tank, h = 8 m
➜ Rate of painting = Rs 5 per m².
Solution : Here, we use formula of volume of cylinder
➜ Volume of tank = πr²h
➜ Volume of tank = (22/7) * (35)² * 8
➜ Volume of tank = (22/7) * 1225 * 8
➜ Volume of tank = 22 * (1225/7) * 8
➜ Volume of tank = 22 * 175 * 8
➜ Volume of tank = 3850 * 8
➜ Volume of tank = 30800 m³
Now, by formula of curved surface area of cylinder;
➜ Curved surface area of tank = 2πrh
➜ Curved surface area of tank = 2 * (22/7) * 35 * 8
➜ Curved surface area of tank = 2 * 22 * (35/7) * 8
➜ Curved surface area of tank = 44 * 5 * 8
➜ Curved surface area of tank = 44 * 40
➜ Curved surface area of tank = 1760 m²
Now, by formula of area of circle;
➜ Area of top of tank = πr²
➜ Area of top of tank = (22/7) * (35)²
➜ Area of top of tank = (22/7) * 1225
➜ Area of top of tank = 22 * (1225/7)
➜ Area of top of tank = 22 * 175
➜ Area of top of tank = 3850 m²
Now,
➜ Cost of painting of curved surface of tank = Curved surface area of tank * Rate of painting
➜ Cost of painting of curved surface of tank = 1760 * 5
➜ Cost of painting of curved surface of tank = Rs 8800
Similarly;
➜ Cost of painting of top of tank = Area of top of tank * Rate of painting
➜ Cost of painting of top of tank = 3850 * 5
➜ Cost of painting of top of tank = Rs 19250
Answer : Hence, volume of the tank is 30800 m³ and the cost of painting of curved surface of tank is Rs 8800 and the cost of painting of top of tank is Rs 19250.