Question

If height of a cylinder is 42cm and radius is 14 cm then
(i) The total surface area area and
(ii) Curved surface area of​

Answer 1

Answer:

Assume we have a right circular cylinder. Flatten it out and you have a rectangle whose width is the same as the height of the cylinder, and whose length is the same as the circumference of the base of the cylinder. As with any rectangle, area = length times width.

The width aka height is 14 cm.

The length aka circumference is = diameter x pi = 42 pi cm

The area of the rectangle aka curved surface of the cylinder is 14 x 42 pi = 588 pi cm^2.

Answer 2

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: Radius \: of \: the \: cylinder = 14cm \\ \\ \sf \: Height \: of \: cylinder = 42cm$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: (i) \: Total \: surface \: area \: of \: cylinder \\ \\ \sf \: (ii) \: Curved \: surface \: area \: of \: cylinder$

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

$\sf \: Total \: surface \: area = 2\pi r(r + h) \\ \\ \sf \: Curved \: surface \: area = 2\pi rh$

$\large{\red{\underline\bold{{Solution:}}}}$

$\sf \: Let \: the \: radius \: of \: the \: cylinder \: be \: r, \\ \sf \: and \: the \: height \: of \: the \: cylinder \: as \: h$

$\large{\green{\bold{\underline{Then:}}}}$

$\sf \: (i) \: Total \: surface \: area = 2\pi r(r + h) \\ \\ \rightarrow \: \sf Total \: surface \: area = 2 \times \frac{22}{7} \times 14(14 + 42) \\ \\ \rightarrow \: \sf Total \: surface \: area = 2 \times \frac{22}{7} \times 14(56) \\ \\ \rightarrow \: \sf \: Total \: surface \: area = \frac{44}{\cancel7} \times \cancel14 \times 56 \\ \\ \rightarrow \: \sf \: Total \: surface \: area = 4928 \: {cm}^{2}$

$\large{\pink{\bold{\underline{Now:}}}}$

$\sf \: (ii) \: Curved \: surface \: area = 2\pi rh \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 2 \times \frac{22}{7} \times 14 \times 42 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 2 \times \frac{22}{\cancel7} \times \cancel14 \times 42 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 44 \times 2 \times 42 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 3696 \: {cm}^{2}$

$\large{\orange{\bold{\underline{Therefore:}}}}$

$\sf \: The \: total \: surface \: area \: of \: cylinder \: is \\ \sf \: 4928 {cm}^{2} \: and \: curved \: surface \: area \: is \: 3696 {cm}^{2}.$