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प्रश्न
A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment.
उत्तर
Depth (h1) of the well = 14 m
Radius (r1) of the circular end of the well =`4/2` m = 2 m
Height (h2) of embankment = 40 cm = 0.4 m
Let the width of embankment be x.
From the figure, it can be observed that the embankment will be cylindrical in shape having outer radius (r2) as (2 + x) m and inner radius (r1) as 2 m.
Volume of earth dug from the well = Volume of earth used to form embankment
`pir_1^2h_1=pi(r_2^2-r_1^2)h_2`
`=>pi(2)^2 14=pi[(2+x)^2-2^2]0.4`
`=>4xx14=(x(x+4)4)/10`
⇒x2+4x−140=0
⇒x2+14x−10x−140=0
⇒(x+14)(x−10)=0
⇒x=10 (Because x cannot be negative)
Therefore, the width of the embankment will be 10 m.
संबंधित प्रश्न
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Assertion (A)
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Reason (R)
The total surface area of a hemisphere is 3π r2.
- Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.
Reason (R)
Volume of a sphere `=4/3pi"R"^3`
Surface area of a sphere = 4πR2
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use π = 3.14)
There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 66 cm long and he takes exactly 400 steps to go around the pond, find the diameter of the pond.
