Question

The length of tape required to cover the edges of a semi-circular disc of radius $10 \mathrm{~cm}$ is: (a) $62.8 \mathrm{~cm}$ (b) $51.4 \mathrm{~cm}$ (c) $31.4 \mathrm{~cm}$ (d) $15.7 \mathrm{~cm}$

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Answer

To determine the length of tape required to cover the edges of a semi-circular disc of radius $10 , \mathrm{cm}$, we need to calculate the perimeter of the semi-circle, which includes its curved edge and the straight diameter.

  1. Calculate the Circumference: For a complete circle, the circumference is given by: $$ 2\pi r $$ However, since we have a semi-circle, the curved edge (or the semi-circumference) will be half of the full circle's circumference: $$ \frac{2\pi r}{2} = \pi r $$ Substituting $r = 10 , \mathrm{cm}$: $$ \pi \times 10 \approx 3.14 \times 10 = 31.4 , \mathrm{cm} $$

  2. Add the Diameter: The diameter of the semi-circle is simply twice its radius: $$ 2 \times 10 , \mathrm{cm} = 20 , \mathrm{cm} $$

  3. Calculate Total Length of Tape Required: Adding the semi-circumference to the diameter gives the total perimeter: $$ 31.4 , \mathrm{cm} + 20 , \mathrm{cm} = 51.4 , \mathrm{cm} $$

Thus, the length of tape needed to cover the entire edges of the semi-circle is $51.4 , \mathrm{cm}$, corresponding to option (b).


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