Question 43

A hollow cylinder has height 90 cm and the outer curved surface area is 11880 cm$$^2$$. It can hold 55440 cm$$^3$$ of air inside it. What is the thickness (in cm) of this cylinder?

Solution

Let say, radius of inside of cylinder = r cm.

So, $$\pi r^2h\ =\ 55440.$$

or, $$r\ =\ 14.$$ (h = 90 cm)

Let say, Curved surface area = $$2\pi h\left(R+r\right)\ .$$

So, $$2\pi h\left(R+r\right)=11880.$$

or, $$\left(R+r\right)=\frac{11880}{2\pi h}=\frac{11880\times7}{2\times22\times90}=21.$$

So, $$R=21-r=21-14=7.$$

Thickness of cylinder is 7 cm.

C is correct choice.

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