A hemi-spherical dome of a building needs to be painted. If the circumference of the base of the dome is $17.6\ m$, find the cost of painting it, given the cost of painting is $Rs.\ 5$ per $100\ cm^2$.

 Given:

A hemi-spherical dome of a building needs to be painted.

The circumference of the base of the dome is $17.6\ m$.

The cost of painting is $Rs.\ 5$ per $100\ cm^2$.

To do:

We have to find the cost of painting the dome.

Solution:

Circumference of the base of the dome $(r) = 17.6\ m$

This implies,

Radius of the dome $=\frac{c}{2 \pi}$

$=\frac{17.6 \times 7}{2 \times 22}$

$=2.8 \mathrm{~m}$

Therefore,

Surface area of the dome $=2 \pi r^{2}$

$=2 \times \frac{22}{7} \times(2.8)^{2}$

$=\frac{44}{7} \times 2.8 \times 2.8$

$=49.28 \mathrm{~m}^{2}$

Rate of painting the surface $=Rs.\ 5$ per $100 \mathrm{~cm}^{2}$

Total cost of painting the dome $=Rs.\ \frac{49.28 \times 5 \times 10000}{100}$

$=Rs.\ 24640$

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Updated on: 10-Oct-2022

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