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Mathematics · Surface Areas and Volumes · NCERT Examples

Example 4

A complete, independently verified solution for NCERT Example 4.

Mathematics · Chapter 12 · NCERT Examples

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NCERT Example

Example 4

bird-bath · hemispherical depression

A bird-bath is a cylinder with a hemispherical depression at one end. The cylinder is 1.45 m high and has radius 30 cm. Find its total surface area. Take π = 22/7.

Cylindrical bird-bath with a hemispherical depression, radius 30 centimetres and height 1.45 metres.
Figure 12-9 from the supplied NCERT chapter.

Solution

Board-exam working:

Use one unit throughout.

h=1.45 m=145 cm,r=30 cmh=1.45\text{ m}=145\text{ cm},\qquad r=30\text{ cm}

The exposed area is the curved surface of the cylinder plus the curved surface of the depression.

A=2πrh+2πr2=2πr(h+r)A=2\pi rh+2\pi r^2=2\pi r(h+r)
=2×227×30×(145+30)=2\times\frac{22}{7}\times30\times(145+30)
=33000 cm2=33000\text{ cm}^2
=3300010000=3.3 m2=\frac{33000}{10000}=3.3\text{ m}^2

Final answer

3.3 m2\boxed{3.3\text{ m}^2}