Question

Surface area of a tunnel is 550 m². The tunnel is a 25 m long cylinder. Find the diameter of the
tunnel.​

Answer 1

Answer :

$\boxed{\boxed{\mathsf{Diameter \: = \: 7m}}}$

Step-by-step Explanation :

Given :

• Surface area of a tunnel is 550 m².
• Length of tunnel = 25m

To find :

• The Diameter of the tunnel .

Solution :

Now according to question,

Now we know that,

$\boxed{\bigstar\: \mathsf{Curved \: Surface\: area\: of \: cylinder = 2 \pi r h}}$

Where here,

$\mathsf{\longrightarrow \: Curved \: Surface \: area \: = 550m^2}$

$\mathsf{\longrightarrow \: r = radius\: = To \: find }$

$\mathsf{\longrightarrow \: h = height \: \longrightarrow \:Length = 25m }$

$\mathsf{\longrightarrow \: And \: taking \: \pi = \dfrac{22}{7}}$

We have,

$\mathsf{\longrightarrow \: 550 m^2 = 2 \times \dfrac{22}{7} \times r \times 25m }$

$\underline{\mathsf{\star \: Taking \: 25m \: LHS \: we \: have..}}$

$\mathsf{\longrightarrow \: \dfrac{550 m^2}{25} = 2 \times \dfrac{22}{7} \times r }$

$\mathsf{\longrightarrow \: 22m = 2 \times \dfrac{22}{7} \times r }$

$\mathsf{\longrightarrow \: 22m = 2 \times \dfrac{22}{7} \times r }$

$\underline{\mathsf{\star \: Taking \: \dfrac{22}{7} \: LHS \: we \: have..}}$

$\mathtt{\longrightarrow \: 22m \times \dfrac{7}{22} = 2 \times \dfrac{22}{7} \times r }$

$\mathsf{\longrightarrow \: 7m \: = 2r }$

$\mathsf{\longrightarrow \: Radius (r) = \dfrac{7m}{2}}$

Now we know that :

$\implies \: \mathsf{Diameter \: = \: 2 \times \: radius }$

$\longrightarrow \: \mathsf{Diameter \: = \: 2 \times \:\bigg(\dfrac{7m}{2}\bigg)}$

$\longrightarrow \: \mathsf{Diameter \: = 7m }$

Therefore Required answer :

$\underline{\boxed{\mathsf{Diameter \: = \: 7m}}}$

$\large \bigstar \: \underline{\blue{\mathfrak{Points \: To \: Remember}} \bigstar }$

$\mathsf{\underline{Cylinder}}$

$\mathsf{\star \: Curved \: Surface \: Area = 2\pi r h}$

$\mathsf{\star \: Total \: Surface \: Area = 2 \pi r(r + h)}$

$\mathsf{\star \: Volume = \pi r^2 h}$

Answer 2

Given :-----

• Surface area of tunnel = 550m²
• length of cylinderical tunnel = 25m
• Diameter of tunnel = ?

Formula used :-----

• CSA of cylinder = 2πrh
• π = 22/7
• diameter of tunnel = 2× radius of tunnel
• length = Height of tunnel

Calculation :------

$2 \times \pi \times r \times h = 550 \\ \\ 2 \times \frac{22}{7} \times r \times 25 = 550 \\ \\ r = \frac{ \cancel{550} \times 7}{2 \times \cancel 22 \times \cancel 25} \\ \\ r = \frac{7}{2} \: m$

$Hence, \: diameter \: of \: tunnel \: = 2 \times \frac{7}{2} \\ \\ diameter = 7 \: m$

(Hope it helps you)