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**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(r_{1}^{2} + r_{2}^{2} + r_{1}r_{2}), where, h = height, r_{1} and r_{2} are the radii(r_{1} > r_{2})

For bucket,

Volume of bucket = 28.490 L

1 L = 1000 cm^{3}

Volume of bucket = 28490 cm^{3}

Radius of top, r_{1} = 28 cm

Radius of bottom, r_{2} = 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(28^{2} + 21^{2} + 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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