Question

A 20 metre deep well with diameter 7m is dug up and the earth from the digging is spread evenly to form a platform 22 m x 14 m. Determine the height of the platform.

Answer 1

${\huge{\underline{\underline{\rm{\bold{QuestiOn:}}}}}}$

A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

${\huge{\underline{\underline{\rm{\bold{SolutiOn:}}}}}}$

$\bf{\red{Given\:that:}}$

The volume of earth removed by digging for cylindrical well is same volume used in making platform which is cuboidal in shape

Therefore,

➠Volume of well dug = Volume of platform formed

✢PARAMETERS FOR WELL✢

Diameter(d) = 7 m

So, radius (r)= d/2 = 3.5 m or 7/2 m

Given, the well is 20 m deep so,we can say that it's height is 20 m

Height (h)=20 m

➠Volume of cylinder = πr²h

Volume of well dug

$= \frac{22}{7} \times { \frac{7}{ {2}^{2} } }^{2} \times 20$

$= \frac{22}{7} \times \frac{49}{4} \times 20 \\ = 22 \times 7 \times 5 \\ = 770 {m}^{3}$

✢PARAMETERS FOR PLATFORM✢

Length (l)= 22 m

breadth (b)=14 m

Let the height be h

Volume of cuboid = l × b × h

⇒ Volume of platform = 22 × 14 × h

= 308h m3

As volume of well dug = volume of platform formed

⇒ 770 = 308h

h=770/308

Divide numerator and denominator by 7 we get,

h=110/44

Divide numerator and denominator by 22 we get,

h=5/2=2.5m

$\bf{\green{Therefore,\:the\: height\:of\: platform\:is\:2.5\:cm}}$

Answer 2

Answer:

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