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A Bucket is in the Form of a Frustum of a Cone and It Can Hold 28.49 Litres of Water. If the Radii of Its Circular Ends Are 28 Cm and 21 Cm, Then Find - Mathematics

Sum

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, then find the height of the bucket.

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Solution

We have,

Radius of upper end, R=28 cm and

Radius of lower end, r = 21 cm

Let the height of the bucket be h.

Now,

Volume of water the bucket can hold = 28.49 L

⇒ Volume of bucket = 28490 cm   (As, 1L = 1000 cm3)

`rArr 1/3pi"h"("R"^2+"r"^2+"Rr") = 28490`    

`rArr 1/3xx22/7xx"h"(28^2+21^2+28xx21) = 28490`

`rArr (22"h")/21xx49xx(16+9+12)=28490`

`rArr (22"h")/3 xx7xx37 = 28490`

`rArr "h" = (28490xx3)/(22xx7xx37)`

∴ h = 15 cm

So, the height of the bucket is 15 cm.

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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise 19C | Q 11 | Page 911
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