Geometry

Solids

Medium

A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively.

What is the volume of clay required for making a tile?

30.24 π cm³

5.76 π cm³

6.76 π cm³

6.96 π cm³

✅ Correct Option: 1

The drainage tile is a cylindrical shell with:

Length = 21 cm
Outside diameter = 5.1 cm
Inside diameter = 4.5 cm

The outside radius $R = \dfrac{5.1}{2} = 2.55$ cm

The inside radius $r = \dfrac{4.5}{2} = 2.25$ cm

The volume of clay is the volume of the outer cylinder minus the volume of the inner cylinder.

Volume of clay $= \pi R^2 h - \pi r^2 h$

$= \pi h (R^2 - r^2)$

Calculate $R^2$ :

$R^2 = (2.55)^2 = 6.5025$

Calculate $r^2$ :

$r^2 = (2.25)^2 = 5.0625$

Find the difference:

$R^2 - r^2 = 6.5025 - 5.0625 = 1.44$

Volume $= \pi \times 21 \times 1.44$

$= 30.24\pi$ cm³

Therefore, the volume of clay required is $30.24\pi$ cm³.

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A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively. What is the volume of clay required for making a tile?

Solution

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CUET General Test Past Year Questions (Topic-Wise)

A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively.

What is the volume of clay required for making a tile?