Question

The circumference of the base of a right circular cylinder is 220 CM. If the height of the cylinder is 2 metre find the lateral surface area of the cylinder?

Answer given on back of the book is = 4.4 metre square.​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

4.4 m^2

$\huge\star{\green{\underline{\mathfrak{Explanation :-}}}}$

Circumference of the base of a right circular cylinder = 220 cm = 2.2 m

Therefore,

$\leadsto {2 \pi \: r = 2.2}$

$\leadsto { 2 \times \dfrac{22}{7} \times r = 2.2}$

$\leadsto { r = 2.2 \times \dfrac{7}{22} \times \dfrac{1}{2}}$

$\leadsto {r = \dfrac{\cancel {22}}{10} \times \dfrac{7}{\cancel {22} } \times \dfrac{1}{2}}$

$\leadsto { r = \dfrac{7}{20} \: m}$

Now, formula for lateral surface area of a cone is :- $2\pi \: r \: h$.

Height given = 2m

Therefore,

$\leadsto {= 2 \times \dfrac{11\: \: \cancel {22}}{7} \times \dfrac{7}{\cancel {20} \: \: \cancel{10 } \: \: 5} \times \cancel {2}}$

$\leadsto {= 4.4 \: {m}^{2} }$

So, the lateral surface area of the cone is 4.4 m^2.

____________________

Answer 2

$\bf{\Huge{\underline{\boxed{\rm{\red{ANSWER\::}}}}}}$

Given:

The circumference of the base of a right circular cylinder is 220cm. If the height of the cylinder is 2m.

To find:

The lateral surface area of the cylinder.

$\bf{\Large{\underline{\sf{\green{Explanation\::}}}}}}}$

We have,

• Circumference= 220cm
• Height of the cylinder,h= 2m

We know that formula of the circumference of circle: 2πr

→ 2πr = 220cm

→ $2*\frac{22}{7} *r=220$

→ $\frac{44}{7} *r=220$

→ $r=(\frac{\cancel{220}*7}{\cancel{44}} )cm$

→ r = (5×7)cm

→ r = 35cm

∴If convert into m then;

$\boxed{\begin{minipage{3cm}\\ 1cm=\frac{1}{100} m\\ \\\end{minipage}}}$

→ r= $\cancel{\frac{35}{100}} m$

→ r= 0.35m

Now,

We know that formula of the lateral surface area of the cylinder:

→ 2πrh    [sq.units]

→ $(2*\frac{22}{7} *0.35*2)m^{2}$

→ $(\frac{44}{7} *0.7)m^{2}$

→ $(\frac{44}{\cancel{7}} * \cancel{0.7})m^{2}$

→ (44× 0.1)m²

→ 4.4m²

Thus,

The lateral surface area of the cylinder is 4.4m².