Question

Which is false?
A metal pipe is 63 cm long. Its inner diameter is 4 cm and the outer diameter is 4.4 cm. Then,
(a) its inner curved surface area = 792 cm²
(b) its outer curved surface area = 871.2 cm²
(c) surface area of each end = 2.64 cm²
(d) its total surface area = 1665.84 cm²

Answer 1

(d) its total surface area = 1665.84 cm²

Height of the metal pipe = 63 cm
Its inner radius = 2 cm
Its outer radius = 2.2 cm

(a) $\mathrm{Inner}\mathrm{curved}\mathrm{surface}\mathrm{area}=2\mathrm{\pi }\times 2\times 63=792{\mathrm{cm}}^2$
Hence, (a) is true.

(b) $\mathrm{Outer}\mathrm{curved}\mathrm{surface}\mathrm{area}=2\mathrm{\pi }\times 2.2\times 63=871.2{\mathrm{cm}}^3$
Hence, (b) is true.

(c) $\mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{each}\mathrm{end}=\mathrm{\pi }\left[\right(2.2{)}^2-2^2]=2.64{\mathrm{cm}}^2$
Hence, (c) is true.
(d)
$$\begin{gathered} \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{pipe}=2\mathrm{\pi }\left(4.4-4\right)\times 63+2\mathrm{\pi }(4.4^2-4^2) \\ =2\times \frac{22}{7}\times \left[0.4\times 63+\left(19.36-16\right)\right] \\ =\frac{44}{7}\times \left[25.2+3.36\right] \\ =\frac{44}{7}\times 28.56 \\ =179.52{\mathrm{cm}}^2 \end{gathered}$$

Hence, (d) is false.