Question

The diameter of a circular wall is 4.5m and it's depth is 14m. find the cost of cementing the inner surface of the wall at ₹120per sq. m​

Answer 1

✬ Cost = Rs 23760 ✬

Step-by-step explanation:

Given:

• Diameter of a circular well is 4.5 m.
• Depth of circular well is 14 m.
• Cost of cementing per sq. m is Rs 120.

To Find:

• What will be the cost of cementing the inner surface area ?

Solution: Radius of well will be

➟ Radius = Diameter/2

➟ Radius = 4.5/2 = 2.25 m

Here the well is to be cemented from inside therefore we have to find the CSA of the well which is in the shape of a cylinder.

As we know that

★ CSA of Cylinder = 2πrh ★

$\implies{\rm }$ CSA of Well = 2(22/7)(2.25)(14)

$\implies{\rm }$ 44(2.25)(2)

$\implies{\rm }$ 44 $\times$ 4.5

$\implies{\rm }$ 198 m²

Now, Cost of cementing 1 m² well = Rs 120

So, Cost of cementing 198 m² well = 198 $\times$ 120

➫ Rs 23760

Hence, total cost will be Rs 23760.

Answer 2

Step-by-step explanation:

$\bf Given:-$

• The diameter of a circular well is 4.5m

• Depth of the circular well is 14m

$\bf To\:Find:-$

• The cost of cementing the inner surface of the well at ₹120per sq.m

$\bf Solution:-$

Diameter of circular well = 4.5m

$\sf radius \: (r) = \dfrac{4.5}{2}$

= 2.25m

Depth (h) of the well = 14m

As we know that:-

$\boxed{ \sf Inner \:curved \: surface\: area \: = 2\pi rh }$

Here:-

• π = 22/7

• r = radius

• h = depth

Substituting the values:-

$\sf \longrightarrow 2 \times \dfrac{22}{7} \times 2.25 \times 14$

$\sf \longrightarrow 2 \times \dfrac{22}{7} \times \dfrac{225}{100} \times 14$

$\sf \longrightarrow 2 \times {22}\times \dfrac{225}{100} \times2$

$\sf \longrightarrow 198 {m}^{2}$

Cost of cementing 1m² = ₹120

Cost of cementing 198m² = 120 × 198 = ₹23760.

Therefore:-

Cost of cementing the inner surface area of the well is ₹23760