Question

Choose the correct answer of the following question:

A rectangular sheet of paper 40 cm $\times$ 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is

(a) 3.5 (b) 7 (c) 80 (d) 5 [CBSE 2014]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{sheet},l=40\mathrm{cm}, \\ \mathrm{Width}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{sheet},b=22\mathrm{cm}\mathrm{and} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{hollow}\mathrm{cylinder},h=40\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{cylinder}\mathrm{be}r. \\ \mathrm{As},l=h \\ \mathrm{So},\mathrm{the}\mathrm{circumference}\mathrm{of}\mathrm{base}\mathrm{of}\mathrm{the}\mathrm{cylinder}=b \\ \Rightarrow 2\mathrm{\pi }r=22 \\ \Rightarrow 2\times \frac{22}{7}\times r=22 \\ \Rightarrow r=\frac{22\times 7}{2\times 22} \\ \therefore r=3.5\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option (a).