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

Solution:

Given, a bucket in the form of a frustum of a cone

The bucket holds 28.490 litres of water.

The radii of the top and bottom are 28 cm and 21 cm.

We have to find the height of the bucket.

Volume of the frustum of a cone = πh/3 (R² + r² + Rr)

Given, R = 28 cm

r = 21 cm

Volume = 28.490 litres of water

= 28.490 × 1000 cm³

Volume of bucket = 28490 cm³

Now, 28490 = πh/3 ((28)² + (21)² + 28(21))

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

28490 = 22h/21 (1813)

Solving for h,

28490 = (39886/21)h

28490 = 1899.33h

h = 28490/1899.33

h = 15 cm

Therefore, the height of the bucket is 15 cm

✦ Try This: A bucket is in the form of a frustum of a cone and holds 30 litres of water. The radii of the top and bottom are 18 cm and 12 cm, respectively. Find the height of the bucket.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.3 Problem 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

Summary:

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. The height of the bucket is 15 cm

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