Question

a plot of 20×30 m² is dugout inside boundary the earth dugout is spread all over the plot due to this the plot height is increased by 20cm if the width dugout boundary is 1m then find the depth of the boundary dugout

Answer 1

Answer:

Solution:-Diameter = 7 m so, radius = 3.5 mH = 20 mVolume of the earth dug out = π

Answer 2

Given :- A plot of 20×30 m² is dugout inside boundary the earth dugout is spread all over the plot due to this the plot height is increased by 20cm if the width dugout boundary is 1m then find the depth of the boundary dug out ?

Solution :-

Let us assume that, the depth of the boundary dug out is x m.

we have,

→ width of dug out boundary = 1 m .

then,

→ Volume of the earth dug out = Volume of all 4 cuboid formed outside = v1 + v2 + v3 + v4

as we can see ,

• v1 = v3
• v2 = v4

so,

→ Volume of the earth dug out = 2v1 + 2v2 = 2(l * b * h) + 2(l * b * h) = 2(32 * 1 * x) + 2(20 * 1 * x) = 64x + 40x = 104x m³.

[ or we can solve it as by finding the outer area and than multiply by depth . => (32 * 22) - (30 * 20) = 704 - 600 = 104 m² .=> volume = 104 * x = 104x m³. ]

now,

→ volume of cuboid so formed of plot = (l * b * h) = 20 * 30 * (20/100) = 600 * (1/5) = 120 m³ .

therefore,

→ volume of the earth dug out = volume of plot

→ 104x = 120

→ x = (120/104)

→ x = 1.15 m (Ans.)

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