#### Question

A hemi-spherical dome of a building needs to be painted. If the circumference of the base of

the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00

`cm^2`

#### Solution 1

Given that only the rounded surface of the dome to be painted, we would need to find the

curved surface area of the hemisphere to know the extent of painting that needs to be done.

Now, circumference of the dome =17.6m.

Therefore, 17.6=2πr.

`2× 22/7r= 17.6m.`

So, the radius of the dome = 17.6× `7/(2× 22)`

m=2.8m

The curved surface area of the dome = `2πr^2`

=`2× 22/7× 2.8× 2.8cm^2`

= `49.28m^2`

Now, cost of painting 100`cm^2` is Rs. 5.

So, cost of painting `1m^2`= Rs.500

Therefore, cost of painting the whole dome

=Rs. 500×49.28

=Rs. 24640 .

#### Solution 2

In the given problem, a hemispherical dome of the building needs to be painted. So, we need to find the surface area of the dome.

Here, we are given the circumference of the hemispherical dome as 17.6 m and as we know that circumference of the hemisphere is given by 2πr. So, we get

`2πr = 17.6`

`2(22/7)r = 17.6`

`r = 17.6 (7/22)(1/2)`

= 2.8

So, now we find the surface area of the hemispherical dome.

` "surface area" = 2 π r^2`

` =2(22/7)(2.8)^2`

= 49.28

So, the curved surface area of the dome is 49.28 m^{2}

Since the rate of the painting is given in cm^{2}, we have to convert the surface area from m^{2} to cm^{2}.

So, we get

Curved surface area = `(49.28)(10000)cm^2`

= 492800 cm^{2}

Now, the rate of painting per 100 cm^{2} = Rs 5

The rate of painting per 1 cm^{2}^{ }= `5/100`

So, the cost of painting the dome = `(5/100) (492800)`

=24640

Therefore, the cost of painting the hemispherical dome of the building is **Rs 24640 .**