Question

$\sf \: Find \: the \: Total \: Surface \: Area \: of \: a \: solid \: cylinder \: of \: radius \: 5cm \: \\ \sf \: and \: height \: 10cm. \: Leave \: your \: answer \: in \: terms \: of \: \pi \: .$




Chapter Name :- Mensuration.​

Answer 1

Answer:

Radius of solid cylinder = 5cm

Height of solid cylinder = 10 cm

Total surface area of solid cylinder = 2πr(h+r)

$\sf \displaystyle \therefore \: 2 \times \frac{22}{7} \times 5(10 + 5)$

$\sf \displaystyle 2 \times \frac{22}{7} \times 5 \times 15$

$\sf \displaystyle \: \frac{3300}{7}$

$= 471.42 \: sq²cm$

Expression of answer in π = 150π (pi) ≈ 471.23

Answer 2

Cylinder - Mensuration

If $r$ be the radius and $h$ be the height of of a solid cylinder, then its total surface area of a solid cylinder is given by,

$\quad\;\boxed{TSA = 2\pi r(h+r)}$

Step-by-step solution:

Given that, the radius is 5cm and height of the solid cylinder is 10cm and we've been asked to find the total surface area of the solid cylinder.

We know that,

$\boxed{\rm{TSA = 2\pi r(h+r)}}$

By substituting the known values in the formula, the following results are achieved:

$\implies TSA = 2\pi \times 5(10 + 5)$

$\implies TSA = 2\pi \times 5(15)$

$\implies TSA = 2\pi \times 75$

$\implies \boxed{\bf{TSA = 150\pi}}$

Hence, the total surface area of a solid cylinder is 150π cm².

$\rule{300}{1}$

Extra Information:

$\boxed{\begin{array}{l}\bigstar\:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf{(1) \:Area\:of\:Base\:and\:top =\pi r^2}\\\\ \sf {(2) \:\:Curved \: Surface \: Area =2 \pi rh}\\\\\sf{(3) \:\:Total \: Surface \: Area = 2 \pi r(h + r)}\\ \\ \sf{(4) \: \:Volume=\pi r^2h}\end{array}}$