Question

How many cubic metres of earth must be dug out
to sink a well 14 m deep and 4 m in diameter?
What will it cost to plaster its inner surface at 2.50
per square metre?
​

Answer 1

Given :

• Depth of well = 14 m
• Diameter of well = 4m
• Rate of plastering inner surface = Rs.2.50 per m²

To find :

• Volume of well
• Cost to plaster inner surface of well

Solution :

Diameter of well = 4m

Radius of well = 4/2 m

Radius of well = 2m

Now,

Volume of dugout = Volume of well

⇒ Volume of well = πr²h

⇒ Volume of well = 22/7 * 2² * 14

⇒ Volume of well = 22 * 4 * 2

⇒ Volume of well = 176 m³           (Required answer)

∴ Volume of well = 176 m³

_________________________________

_________________________________

Rate of plastering :

At first finding area of inner surface which has to be plastered :

CSA of cylinder = 2πrh

⇒ CSA of inner surface of well = 2 * 22/7 * 2 * 14

⇒ CSA of inner surface of well = 2 * 22 * 2 * 2

⇒ CSA of inner surface of well = 176 m²

Now we know,

Cost of plastering = Rate * Area

⇒ Cost of plastering = 2.50 * 176

⇒ Cost of plastering = Rs. 440             (Required answer)

Therefore,

Cost of plastering inner surface = Rs. 440

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

• How many cubic metres of earth must be dug out to sink a well 14 m deep and 4 m in diameter ? What will it cost to plaster it's inner surface at 2.50 per square metre?

★═════════════════★  

♣ ᴛᴏ ꜰɪɴᴅ :

• Volume of well

• Cost to plaster inner surface of well

★═════════════════★  

♣ ɢɪᴠᴇɴ :

• Depth of well = 14 m
• Diameter of well = 4m
• Rate of plastering inner surface = ₹  2.50 per m²

★═════════════════★  

♣ ᴀɴꜱᴡᴇʀ :

• Volume of well = 176 m³

• Cost of plastering : ₹ 440  

★═════════════════★

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

Diameter = 4 m (Given)

Diameter : The length of a straight line through the center of a circle and it's twice the value of radius

Radius : A straight line from the centre to the circumference of a circle or sphere, it is half of diameter.

As we learnt Radius is half of Diameter,

We get Radius = 4/2 m = 2 m

⇒ Volume of well = πr²h

Where:

r = radius

h = height or depth

➠ Height = 14 m

So,

⇒ Volume of well = π × r² × h

⇒ Volume of well = π × r × r × h

⇒ Volume of well = (22/7) × 2 m × 2 m × 14 m

⇒ Volume of well = (22/7) × 56 m³

⇒ Volume of well = 22 × 8 m³

⇒ Volume of well = 176 m³

__________________________-

What do we need to find now ??

Ya, it's cost to plaster its inner surface

Can we get the required cost drectly ?

No

Here's what you do :

Cost of plastering : Price  of plastering per m² × Area

⇒  Area of curved surface = 2πrh

⇒  Area of curved surface = 2 × (22/7) × 2 m × 14 m

⇒  Area of curved surface = 44/7 × 28 m²

⇒  Area of curved surface = 1232/7  m²

⇒  Area of curved surface = 176  m²

As already said :

Cost of plastering : Price of plastering per m² × Area

⇒ Cost of plastering : ₹ 2.50 × 176  

⇒ Cost of plastering : ₹ 440  

∴  176 m² of earth needs to be dug out and the cost of plastering is ₹ 440