Question

The curved surface area of a water tank is 2ᴨ (y2 – 7y + 12) and its radius is (y – 3). The cleaner of the tank wants to know the height of the tank so that he an arrange a ladder to reach the top of the tank and clean it. Help him find the height of the tank.​

Answer 1

The water tank is in the shape of a cylinder.

Given:-

the CSA of the tank = 2π (y^2 - 7y + 12)

the radius of the tank = (y - 3)

Solution:-

CSA of a cylinder = 2πrh

$Height \: of \: the \: cylinder \: = \frac{CSA \: of \: the \: cylinder}{2\pi \times Radius \: of \: the \: cylinder} \\ = \frac{2\pi( {y}^{2} - 7y + 12) }{2\pi(y - 3) } \\ = \frac{ {y}^{2} - 7y + 12}{y - 3} \\ = \frac{ {y}^{2} - 3y - 4y + 12}{(y - 3)} \\ = \frac{ y(y - 3) - 4(y - 3) }{(y - 3)} \\ = \frac{(y - 3)(y - 4)}{(y - 3)} \\ = (y - 4) \: \:$

Thus, the height of the cylinder = (y - 4).