Question

Estimate the cost of painting the inner
wall of a well, if the depth of the well is
14 ft and the diameter is 8 ft. The cost of
painting 2.5 sq. ft is * 20.​

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\green{\mapsto \: \: \: Have \; a \; glance \; at \; it \; before \; solving \; !!}}}}$

Here the concept of CSA of the cylinder has been used. We know that for painting a well, we need to just find the inner curved surface area which is going to be painted since the bases are neglected for painting because well is in the shape of cylinder. Then, if we find the curved surface area of Well and then multiply ut with the rate, we can find the whole value.

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★ Formula Used :-

$\: \large{\boxed{\boxed{\sf{\blue{CSA \: of \: the \: Cylinder \: = \: \bf{2 \: \times \: \pi rh}}}}}}$

$\: \large{\boxed{\boxed{\sf{\blue{Total \: cost \: of \: painting \: = \: \bf{Rate \: \times \: Area \: to \: be \: painted}}}}}}$

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★ Question :-

Estimate the cost of painting the inner wall of a well, if the depth of the well is 14 ft and the diameter is 8 ft. The cost of painting 2.5 sq. ft is 20.

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★ Solution :-

Given,

» Depth of the wall = h = 14 feet

» Diameter of the well = d = 8 feet

We know that, Diameter = 2 × radius

• Radius of well = r = ½ × d = ½ × 8 feet = 4 feet

» Cost of painting 2.5 sq. feet = ₹ 20

Then, using unitary method,

• Cost of painting per sq. feet = ₹ 20/2.5 = ₹ 8

Now according to the question :-

$\: \large{\sf{\purple{\Longrightarrow \: \: \: CSA \: of \: the \: Cylinder \: = \: \tt{\orange{2 \: \times \: \pi rh}}}}}$

$\: \\ \large{\sf{\purple{\Longrightarrow \; \; \; CSA \: of \: the \: Cylinder \: = \: \tt{\orange{2 \: \times \: \dfrac{22}{7} \: \times \: 4 \: \times \: 14}}}}}$

➣ CSA of well = 2 × 22 × 4 × 2 = 352 ft²

$\: \\ \qquad \qquad \large{\boxed{\boxed{\it{CSA \: of \: the \: Well \: = \: \bf{352 \: feet^{2}}}}}}$

Then total cost of painting :-

$\: \\ \large{\boxed{\boxed{\rm{\pink{Total \: cost \: of \: painting \: = \: \bf{\red{Rate \: \times \: Area \: to \: be \: painted}}}}}}}$

➣ Total cost of Painting = ₹ 8 per ft² × 352 ft²

Cancelling ft² both sides, we get,

➣ Total cost of painting = ₹ 2816

$\: \large{\underline{\underline{\rm{\green{\leadsto \; \; Thus, \: the \: total \: cost \: of \: painting \: the \: well \: is \: \boxed{\underline{\bf{\blue{Rs. \: 2816}}}}}}}}}$

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$\: \qquad \large{\underbrace{\mapsto \: \: \: Let's \: understand \: more \: formulas \: :-}}$

$\: \leadsto \: \: \: \it{Volume \: of \: Cylinder \: = \; \sf{\pi r^{2}h}}$

$\: \leadsto \: \: \: \it{Volume \: of \: cone \: = \: \sf{\dfrac{1}{3} \: \times \: \pi r^{2}h}}$

$\: \leadsto \: \: \: \it{Volume \: of \: Sphere \: = \: \sf{\dfrac{4}{3} \: \times \: \pi r^{3}}}$

$\: \leadsto \: \: \: \it{Volume \: of \: Hemisphere \: = \: \sf{\dfrac{2}{3} \: \times \: \pi r^{3}}}$

$\: \leadsto \: \: \: \it{Volume \: of \: Cube \: = \: \sf(Side)^{3}}$

$\: \it{\leadsto \: \: \: Volume \: of \: Cuboid \: = \: \sf{Length(L) \: \times \: Breadth(B) \: \times \: Height(H)}}$

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

• Estimate the cost of painting the inner  wall of a well, if the depth of the well is  14 feet and the diameter is 8 feet. If the cost of  painting 2.5 sq. ft is ₹20.​

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♣ ɢɪᴠᴇɴ :

• Depth of the well is  14 feet

• Diameter is 8 feet

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♣ ᴛᴏ ꜰɪɴᴅ :

• The cost of painting the inner  wall of a well

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♣ ᴀɴꜱᴡᴇʀ :

• Cost of painting the inner  wall of a well =  ₹2816

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

Diameter = 8 feet (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 = 8/2 feet = 4 feet

Cost of painting the inner  wall of a well =

Price of painting inner wall per sq. feet  × C.S.A

⇒  Area of curved surface = 2πrh

Where:

r = radius

h = height or depth

⇒  Area of curved surface = 2πrh

⇒  Area of curved surface = 2 × (22/7) × 4 feet × 14 feet

⇒  Area of curved surface = 44/7 × 56 sq. ft

⇒  Area of curved surface = 2464/7  sq. ft

⇒  Area of curved surface = 352 sq. ft

Hence Cost of painting the inner  wall of a well

= ₹20 × 352 sq. ft

= ₹20/2.5 sq. ft  × 352 sq. ft

= ₹20/2.5 × 352

= ₹8 × 352

= ₹2816