Question

8. How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m
diameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per m2.​

Answer 1

$\boxed{\huge{\red{Questions:-}}}$

Q.How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 mdiameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per m2.

$\boxed{\huge{\Green{Answer:-}}}$

◻ The volume of the well is 594 m³.The cost of plastering of inner surface of well

is ₹ 3792.

$\boxed{\huge{\blue{Calculation:-}}}$

H =21 m

D= 6m

R = 6/2m=3m

Volume of cylinder =

$volume \: of \: cylinder = \pi \: r ^{2} h$

$= \frac{22}{7} \times 3 \times 3 \times 21$

$= 594 {m}^{2}$

Cost = Rate × CSA

$=> 9.50 \: per \: {m}^{2} \times 2\pi \: r \: h$

$= > 9.50 \times 2 \times \frac{22}{7} \times 3 \times 21$

Cost => ₹ 3762

Hence, Solved.

Answer 2

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❏ Question:-

How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m

diameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per m2.

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❏ Solution:-

Figure :-

$\setlength{\unitlength}{1 cm}\begin{picture}(12,4)\thicklines\put(2.7,2.7){ . }\put(6,3){\circle{2}}\put(6,6){\circle{2}}\put(6,3){\line(0,1){3}}\put(5.3,3){\line(0,1){3}}\put(6.7,3){\line(0,1){3}}\put(6,3){\line(1,0){0.7}}\put(6,6){\line(1,0){0.7}}\put(6.1,6.13){ 3 \:m }\put(6.8,4.5){ 21\:m }\end{picture}$

✏ Given:-

• deepness(h) of the sink = 21 m.
• diameter(d) of the sink = 6 m.
• Radius (r) = $\sf{\ \ {\dfrac{\cancel6}{\cancel2}}}$ = 3 m.
• Cost of plastering at a rate = 9.50 Rs/m²

✏ To Find:-

• Cost of plastering the inner surface of the cylindrical well ,

✏ Explanation :-

Here we have to find the inner lateral surface area of the cylindrical well ,

$\implies\sf{\ \ {L.S.A.= 2\pi r h}}$

$\implies\sf{\ \ {L.S.A.= 2\times\dfrac{22}{\cancel7}\times3\times\cancel{21}}}$

$\implies\sf{\ \ {L.S.A.= 2\times22\times3\times3}}$

$\implies\boxed{\sf{\ \ {L.S.A.=396\: meters }}}$

Hence

∴ the cost of plastering the inner surface of the well = (396×9.50) Rs. = 3762 Rs.

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