Question

The cost of polishing the total surface area of a closed cylindrical oil tank at 25 paise per decimeter square is 77 rupees. It's height is 3 times that the radius of its base.detrermine the radius of the base and height

Answer 1

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Answer 2

The radius of the base is 3.5 dm and height is 10.5 dm.

The cost of polishing the total surface area of a closed cylindrical oil tank at 25 paise per dm² is 77 Rs. Its height is 3 time that the radius of its base.

We have to find the radius of the base and height.

let radius of the base is r then height of tank is 3r.

∴ total surface area of cylindrical oil tank = 2 × base area + curve surface area

= 2 × πr² + 2πr(3r)

= 2πr² + 6πr²

= 8πr²

total surface area = total cost/rate of polishing

= (77Rs.)/(25p/dm²)

= (77Rs)/(25/100 Rs/dm²)

= 77 × 4 dm²

= 308 dm²

∴ total surface area of cylindrical oil tank = 308 = 8πr²

⇒308 = 8 × 22/7 × r²

⇒(308 × 7)/(22 × 8) = r²

⇒r² = 49/4

⇒r = 7/2 = 3.5 dm

and height = 3r = 21/2 = 10.5 dm

Therefore the radius of the base is 3.5 dm and height is 10.5 dm.