Question

From a sheet of area 8 square metres, a closed cylindrical tank is formed which has one-metre height and 140 cm diameter. How much area of the sheet will be left after making the tank?

Answer 1

Hint: Assume that the area of the sheet remaining is x square centimetres. Use the fact that the curved surface area of a cylinder of radius r and height h is given by $A=2\pi rh$. Since the cylinder is closed, we need to consider both the area of the bottom and the area of the top. Use the fact that the area of a circle of radius r is equal to $\pi {{r}^{2}}$. Use the fact that the area required to make the cylinder and the area of the sheet remaining is equal to the total area of the sheet and hence form an equation in x. Solve for x and hence find the area of the sheet remaining.

Complete step-by-step answer:
Let the area of the sheet remaining be x square centimetres.

We know that the curved surface area of a cylinder of radius r and height h is given by $CSA=2\pi rh$
Here the diameter of the base of the cylinder = 140cm
Hence the radius of the base of the cylinder(r) $=\dfrac{140}{2}=70cm$
Height of the cylinder(h) = 1m = 100cm
Hence the curved surface area of the cylinder $=2\pi rh=2\times \dfrac{22}{7}\times 70\times 100=44000c{{m}^{2}}$
Also, we have
Area of the top of the cylinder $=\pi {{r}^{2}}=\dfrac{22}{7}\times 70\times 70=15400c{{m}^{2}}$ and the area of the bottom of the cylinder $=\pi {{r}^{2}}=\dfrac{22}{7}\times 70\times 70=15400c{{m}^{2}}$
Hence the total area of the sheet required to make the cylinder = 44000+15400+15400=74800 square centimetres.
Also, the area of the sheet is 8 square metres = 80000 square centimetres.
Hence, we have
x+78400 = 80000
Subtracting 78400 from both sides of the equation, we get
x= 80000-78400 =1600 square centimetres
Hence the area of the sheet remaining is equal to 1600 square centimetres.
Note: In the questions of mensuration, students usually make a mistake in taking care of the units. For finding area, volume, length etc., it should be ensured that the units of all the terms included be same and or similar