Find the lateral curved surface area of a cylindrical petrol storage tank that is 4.3 m in diameter and 4.5 m high. How much steel was actually used, if 1/12 of steel actually used was wasted in making the closed tank?
Answers
Given: A cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.
Height of cylindrical tank , h = 4.5 m
Radius of cylindrical tank, (r) = (4.2/2) = 2.1 m
(i) Lateral or curved surface area of tank = 2πrh
= 2 × 22/7 × 2.1 × 4.5
= 2 × 22 × 0.3 × 4.5
= 44 × 0.3 × 4.5
= 59.4 m²
Hence, the lateral or curved surface area of tank = 59.4 m²
(ii) Total surface area of tank = 2πr (r + h)
= 2 × 22/7 × 2.1 × (2.1 + 4.5)
= 44 × 0.3 × 6.6
Total surface area of tank = 87.12 m²
Let the actually used steel in making the tank = x m²
Since, 1/12 of the actual steel used was wasted .
Therefore,
Total surface area of tank = amount of steel - the amount of steel used
87.12 m² = x - x/12
x (1 - 1/12) = 87.12
x(11/12) = 87.12
x = (12/11 × 87.12)
x = 1045.44/11
x = 95.04 m²
Hence, 95.04 m² steel was used in making a tank.
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