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Mathematics · Surface Areas and Volumes · NCERT Examples

Example 2

A complete, independently verified solution for NCERT Example 2.

Mathematics · Chapter 12 · NCERT Examples

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NCERT Example

Example 2

cube and hemisphere · total surface area

A decorative block is made of a cube of edge 5 cm with a hemisphere of diameter 4.2 cm fixed on top. Find its total surface area. Take π = 22/7.

Decorative block formed by a hemisphere of diameter 4.2 centimetres on a cube of edge 5 centimetres.
Figure 12-7 from the supplied NCERT chapter.

Solution

Board-exam working:

r=4.22=2.1 cmr=\frac{4.2}{2}=2.1\text{ cm}

The circular part of the cube covered by the hemisphere is not exposed.

A=6a2−πr2+2πr2A=6a^2-\pi r^2+2\pi r^2
=6(5)2+π(2.1)2=6(5)^2+\pi(2.1)^2
=150+227×2.1×2.1=150+\frac{22}{7}\times2.1\times2.1
=150+13.86=163.86 cm2=150+13.86=163.86\text{ cm}^2

Final answer

163.86 cm2\boxed{163.86\text{ cm}^2}