Question

The height of a cylinder is 3.5 cm and the volume is 110 cu.cm. Find the radius and surface area of this cylinder.​

Answer 1

Step-by-step explanation:

Height (h) of Cylinder = 3.5 cm (Given)

Volume of Cylinder = 110 cm³ (Given)

Volume of Cylinder = πr²h = 110 cm³

∴ πr²h = 110

(Here, π = 22/7 ; r = radius and h = 3.5 cm)

By putting the value in equation -

$\frac{22}{7} *r^{2} *3.5 = 110$

$r^{2} =\frac{110}{3.5} *\frac{7}{22}$

$r^{2} =\frac{1100}{35} *\frac{7}{22} =\frac{50}{5}$

[tex]r^{2} =\frac{50}{5} =10\\ r=\sqrt{10} [/tex]

Total surface area = 2πrh+2πr²

= 2πr(h+r)

=2×22/7*√10(3.5+√10)

= 44√10/7(3.5+√10)

=$\frac{44\sqrt{10} }{7} *3.5+\frac{44\sqrt{10} }{7} *\sqrt{10}$

=$\frac{44\sqrt{10} }{7} *\frac{35}{10} +\frac{44\sqrt{10} }{7} *\sqrt{10}$

$22\sqrt{10} +\frac{440}{7} =\frac{154\sqrt{10} }{7} +\frac{440}{7} =\frac{154\sqrt{10}+440 }{7} =\frac{22(7\sqrt{10}+20) }{7}\\\\=3.14(7\sqrt{10} +20)=21.98\sqrt{10} +62.8=21.98*3.162+62.8 = 69.5+62.8=132.3$