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NCERT Exemplar Solutions Class 10 Mathematics Solutions for Surface Areas and Volumes - Exercise 12.3 in Chapter 12 - Surface Areas and Volumes

Question 9 Surface Areas and Volumes - Exercise 12.3

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Answer:

According to the question,

The bucket is in the form of frustum of a cone.

We know that,

Volume of frustum of a cone = 1/3 πh(r12 + r22 + r1r2), where, h = height, r1 and r2 are the radii(r1 > r2)

For bucket,

Volume of bucket = 28.490 L

1 L = 1000 cm3

Volume of bucket = 28490 cm3

Radius of top, r1 = 28 cm

Radius of bottom, r2 = 21 cm

Let the height = h.

Substituting these values in the equation to find the volume of bucket,

We have.

Volume of bucket = 1/3 πh(282 + 212 + 28(21))

28490 = 1/3 × 22/7 × h (784 + 441 + 588) = 22/7 × h × 1813

⇒ h = (28490 × 21) / (22 × 1813)

⇒ h = 15 cm

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