The cost of painting the total outer surface of a closed cylindrical o

1.	The cost of painting the total outer surface of a closed cylindrical oil tank at 60 paise per sq. \( cm \) is Rs. \( 237.60 \). The height of the tank is 6 times the radius of the base of the tank. Find the height and the radius of the tank.
Answer» \(h = 6r\) \(\therefore TSA = 2\pi rh + 2\pi r^2\) \(= 12\pi r^2 + 2\pi r^2\) \(= 14\pi r^2\) \(= 14 \times \frac {22}7 \times r^2 = 44r^2\) \(\because \) Cost of painting on 1cm² = 60 paise = ₹0.60 \(\therefore \) Cost of painting on 44r² cm² = ₹0.60 x 44 r² But given that cost of painting of closed cylindrical tank = Rs 237.6 \(\therefore 44 r^2 \times 0.6 = 237.6\) ⇒ \(44r^2 = \frac{237.6}{0.6}\) ⇒ \(r^2 = \frac {237.6}{0.6} \times \frac1{44} = \frac{2376}6 \times \frac1{44} = 9\) \(\therefore r = 3 cm\) & \(h = 6r = 18 cm\).

The cost of painting the total outer surface of a closed cylindrical oil tank at 60 paise per sq. \( cm \) is Rs. \( 237.60 \). The height of the tank is 6 times the radius of the base of the tank. Find the height and the radius of the tank.

Answer»

\(h = 6r\)

\(\therefore TSA = 2\pi rh + 2\pi r^2\)

\(= 12\pi r^2 + 2\pi r^2\)

\(= 14\pi r^2\)

\(= 14 \times \frac {22}7 \times r^2 = 44r^2\)

\(\because \) Cost of painting on 1cm² = 60 paise = ₹0.60

\(\therefore \) Cost of painting on 44r² cm² = ₹0.60 x 44 r²

But given that cost of painting of closed cylindrical tank = Rs 237.6

\(\therefore 44 r^2 \times 0.6 = 237.6\)

⇒ \(44r^2 = \frac{237.6}{0.6}\)

⇒ \(r^2 = \frac {237.6}{0.6} \times \frac1{44} = \frac{2376}6 \times \frac1{44} = 9\)

\(\therefore r = 3 cm\)

& \(h = 6r = 18 cm\).

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