Question

A hemispherical dome of a building needs to be painted. If the circumference of the base of the

Come is 17.6 m, find the cost of painting it, given the cost of painting is 5 per 100 cm".

Answer 1

CSA = 49.28 m²

Cost = ₹24640

Explanation:

Since only the rounded surface of the dome is 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 = 17.6 m . Therefore, 17.6 = 2πr .

So, the radius of the dome = 17.6 × 7

2 × 22

= 2.8 m

The Curved surface area of the dome = 2πr²

= 2 × 22/7× 2.8 × 2.8

= 49.28 m²

Now, the cost of painting is 100cm² is ₹5

So, the cost of painting 1m² = ₹500

Therefore, cost of painting the whole dome

= 500 × 49.28

= ₹24640

Answer 2

The cost of painting the hemispherical dome is 110880 unit

Explanation:

Given as for a hemispherical dome :

The circumference of base = 17.6 m

The cost of painting it = 5 unit per 100 cm²

∵ circumference of base = circumference of circle = 2×
`\pi`×radius

So ,17.6 m = 2×
`\pi`×radius

Or, Radius =
`(17.6* 7)/(2* 22)`

Or, Radius =
`(123.2)/(44)` = 2.8 m

Or, R = 280 cm

So, Total surface area of hemispherical dome = 3×
`\pi`×radius²

or, Total surface area of hemispherical dome = 3×
`\pi`×280²

Or, Total surface area of hemispherical dome =
`(3* 22* 280* 280)/(7)`

Or, Total surface area of hemispherical dome =
`(5174400)/(7)`

∴ Total surface area of hemispherical dome = 739200 cm²

Now, The cost of painting 100 cm² is 15 unit

So, The cost of painting 739200 cm² =
`(15* 739200)/(100)`

Or, The cost of painting 739200 cm² = 110880 unit

Hence The cost of painting the hemispherical dome is 110880 unit Answer