Water Storage Tank

Geometry Level 1

The city council is planning to install a new cylindrical water storage tank and needs to know how much paint the side of the tank will need. They can't decide how big the tank will be but they know they want the height of the tank to be equal to the radius. What formula could they use, dependent on the radius, to find the surface area of the side of the water tank?

\pi r^4

2 \pi r h^2

\pi^2

2 \pi r^2

2 solutions

Michael B Staff
Jul 21, 2016

If you unroll a cylinder, the side becomes a rectangle. The area of a rectangle is base times height. You are given that the height of the rectangle is the radius r.

It is slightly more tricky to find the base. Remember that since a cylinder is round it's base is circumferential. Therefore the base is $2*\pi*r\, .$

Once we multiply the base and the height we have the formula $2*\pi*r^2\, .$

One of the only easy solutions. Thanks! 😊

The Humble Believer - 4 years, 10 months ago

Keith Sanchez
Aug 23, 2016

The surface area of the side of the water tank is the same as finding the lateral surface of the cylindrical tank and not the whole surface area of the cylindrical tank (since the whole surface area includes the area of the base).

The formula in finding the lateral surface of the cylindrical tank is: $2 \pi r h$

And since $h=r$ , then the formula will be equal to:

$2 \pi r \cdot r = 2 \pi r^2$

Water Storage Tank

2 solutions

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