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Solution for 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` - CBSE Class 9 - Mathematics

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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

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 .

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Solution 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` Concept: Surface Area of a Sphere.
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