Answer
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Hint: Use the fact that a kaleidoscope is a cylindrical device with each of its circular ends fitted with reflecting surfaces like mirrors. Also, use the formula of the curved surface of a cylinder.
Complete step-by-step solution -
Let us start by drawing a representative figure for better visualisation.
Before we start with the solution, let us discuss about kaleidoscope. A kaleidoscope is an optical instrument generally used to show beautiful designs formed by the repetition of the same artistic elements in a symmetrical form. It is cylindrical in shape, hollow from inside, and contains two reflecting surfaces at its two ends.
Now according to the question, we need to find the curved surface area of the cylindrical kaleidoscope as the area of chart paper needed is equal to the curved surface area of the cylinder. We know that the curved surface area of a cylinder is $2\pi $ times the product of its length and radius..
$\therefore $ The curved surface area of cylinder = $=2\pi rh=2\pi \times 3.5\times 25=175\pi \text{ c}{{\text{m}}^{2}}$
Now, as given in the question, we will put the value of $\pi $ equal to $\dfrac{22}{7}$ . On doing so, we get
The curved surface area of cylinder = $=175\pi =175\times \dfrac{22}{7}=550\text{ c}{{\text{m}}^{2}}$
Therefore, the area of the chart paper required is $550\text{ c}{{\text{m}}^{2}}$ . Hence, the answer to the above question is option (c).
Note: Make sure to convert all the dimensions to a standardized system of units; this decreases the chance of errors. It would also help if you remembered all the basic formulas for surface area and volume of the general 3-D shapes like the cone, cube, cylinder, etc.
Complete step-by-step solution -
Let us start by drawing a representative figure for better visualisation.
Before we start with the solution, let us discuss about kaleidoscope. A kaleidoscope is an optical instrument generally used to show beautiful designs formed by the repetition of the same artistic elements in a symmetrical form. It is cylindrical in shape, hollow from inside, and contains two reflecting surfaces at its two ends.
Now according to the question, we need to find the curved surface area of the cylindrical kaleidoscope as the area of chart paper needed is equal to the curved surface area of the cylinder. We know that the curved surface area of a cylinder is $2\pi $ times the product of its length and radius..
$\therefore $ The curved surface area of cylinder = $=2\pi rh=2\pi \times 3.5\times 25=175\pi \text{ c}{{\text{m}}^{2}}$
Now, as given in the question, we will put the value of $\pi $ equal to $\dfrac{22}{7}$ . On doing so, we get
The curved surface area of cylinder = $=175\pi =175\times \dfrac{22}{7}=550\text{ c}{{\text{m}}^{2}}$
Therefore, the area of the chart paper required is $550\text{ c}{{\text{m}}^{2}}$ . Hence, the answer to the above question is option (c).
Note: Make sure to convert all the dimensions to a standardized system of units; this decreases the chance of errors. It would also help if you remembered all the basic formulas for surface area and volume of the general 3-D shapes like the cone, cube, cylinder, etc.
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