Question

A well, whose diameter is 4 metre has been dug 18 Deep and the earth dug out is used to form an embankment 8 metre wide around it. find the height of embankment

Answer 1

Answer:

0.75 m

Step-by-step explanation:

Refer to the attachment for the figure..

Diameter of well = 4 m

Thus, Radius of well, r = 4/2 = 2 m

Given width of embankment, w = 8 m

So, Radius of Embankment, R = w + r = 8 + 2 = 10 m

Height of Well, H = 18 m

Let the height of the embankment be h m.

Acc. to Que,

Volume of well = vol of soil used in making the embankment

$\implies \pi r^2 H = \pi R^2 h - \pi r^2 h\\\\\implies \pi r^2 H = \pi h (R^2 - r^2)\\\\\implies r^2H = h(R+r)(R-r)\\\\\implies 2 \times 2 \times 18 = h(10 + 2)(10 - 2)\\\\\implies 72 = h \times 12 \times 8\\\\\implies h = \dfrac{72}{12 \times 8}\\\\\\\implies h = 6 \div 8 = 3 \div 4 \\\\\implies \boxed{\bold{h = 0.75 m}}$

Answer 2

Question:-⤵️

A well, whose diameter is 4 metre has been dug 18 Deep and the earth dug out is used to form an embankment 8 metre wide around it. find the height of embankment

Answer:-⤵️

0.75 m

Step-by-step explanation:

the figure..Diameter of well = 4 mThus, Radius of well, r = 4/2 = 2 mGiven width of embankment, w = 8 mSo, Radius of Embankment, R = w + r = 8 + 2 = 10 mHeight of Well, H = 18 mLet the height of the embankment be h m.Acc. to Que,Volume of well = vol of soil used in making the embankment$\implies \pi r^2 H = \pi R^2 h - \pi r^2 h\\\\\implies \pi r^2 H = \pi h (R^2 - r^2)\\\\\implies r^2H = h(R+r)(R-r)\\\\\implies 2 \times 2 \times 18 = h(10 + 2)(10 - 2)\\\\\implies 72 = h \times 12 \times 8\\\\\implies h = \dfrac{72}{12 \times 8}\\\\\\\implies h = 6 \div 8 = 3 \div 4 \\\\\implies \boxed{\bold{h = 0.75 m}}$

❣️Hope this help you ❣️