A well was dug, whose ratio of area of the mouth and the entire page (except the mouth) is 7: 47, if the entire surface area of the well is 258.5 square meters, how much soil came out of the well?
Answers
310.96 m³ of soil came out of the well.
Step-by-step explanation:
Step 1:
Given that,
[Area of the mouth of the well] / [Area of the entire well except for the mouth] = 7:47
i.e., [πr²] / [πr² + 2πrh] = 7/47
⇒ [πr²] / [πr(r + 2h)] = 7/47
⇒ [r] / [r + 2h] = 7/47
⇒ 47r = 7r + 14h
⇒ 40r = 14 h
⇒ h = [40/14] * r
⇒ h = [20r/7] ……… (i)
Step 2:
Also given that,
The entire surface area i.e., total surface area of the well = 258.5 m²
i.e., 2πr² + 2πrh = 258.5
⇒ 2πr [r + h] = 258.5
⇒ 2 * (22/7) * r * [r + (20r/7)] = 258.5 …… [substituting from (i)]
⇒ 2 * (22/7) * r * 3.85r = 258.5
⇒ 24.2 r² = 258.5
⇒ r² = 10.68
⇒ r = 3.26 m ….. (ii)
∴ h = [20 * 3.26]/ [7] = 9.31 m ….. (iii)
Step 3:
Thus, substituting from (ii) & (iii), we get
The amount of soil that came out from the soil is given by,
= Volume of the entire well
= πr²h
= (22/7) * (3.26)² * 9.31
= 310.96 m³
------------------------------------------------------------------------------------------
Also View:
A well is dug whose diameter is 4m and the depth is 10m find the quantity of earth taken out calculate the cost of plastering the curved (inner) surface at rupees 5.00 per square. cm .
https://brainly.in/question/1090985
A well with 14m inner diameter is 8m deep.the earth dug of it has been evenly spread out on rectangular plot of size 10m*8m.find height of earth on plot....
https://brainly.in/question/8338126