The length of tape required to cover the edges of a semicircular disc of radius 10 cm is: (a) 62.8 cm (b) 51.4 cm (c) 31.4 cm (d) 15.7 cm
Question
The length of tape required to cover the edges of a semicircular disc of radius $10 \mathrm{~cm}$ is: (a) $62.8 \mathrm{~cm}$ (b) $51.4 \mathrm{~cm}$ (c) $31.4 \mathrm{~cm}$ (d) $15.7 \mathrm{~cm}$
✨ Free AI Tools for You
Powered by Chatterbot AI
Answer
To determine the length of tape required to cover the edges of a semicircular disc of radius $10 , \mathrm{cm}$, we need to calculate the perimeter of the semicircle, which includes its curved edge and the straight diameter.

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

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

Calculate Total Length of Tape Required: Adding the semicircumference 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 semicircle is $51.4 , \mathrm{cm}$, corresponding to option (b).
India's 1^{st} AI Doubt Solver for CBSE, JEE, and NEET
Ask a Question for Freeand then it's just ₹212 a month