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A Dome of a Building is in the Form of a Hemisphere. from Inside, It Was White-washed at the Cost of Rs 498.96. If the Cost of White-washing is Rs 2.00 per Square Meter, Find the - CBSE Class 9 - Mathematics

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Question

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square meter, find the

(i) inside surface area of the dome,

(ii) volume of the air inside the dome.

`["Assume "pi=22/7]`

 

Solution

(i) Cost of white-washing the dome from inside = Rs 498.96

Cost of white-washing 1 m2 area = Rs 2

Therefore, CSA of the inner side of dome = (498.96/2) m2 = 249.48 m2

 

(ii) Let the inner radius of the hemispherical dome be r.

CSA of inner side of dome = 249.48 m2

r2 = 249.48 m2

`rArr2xx22/7 xxr^2=249.48 m^2`

`rArr r^2=((249.48xx7)/(2xx22))m^2 = 39.69 m^2`

⇒ r = 6.3 m

Volume of air inside the dome = Volume of hemispherical dome

`=2/3pir^3`

`=[2/3xx22/7xx(6.3)^3]m^3`

= 523.908 m3

= 523.9 m3 (approximately)

Therefore, the volume of air inside the dome is 523.9 m3.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 13: Surface Area and Volumes
Ex. 13.80 | Q: 8 | Page no. 236

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Solution A Dome of a Building is in the Form of a Hemisphere. from Inside, It Was White-washed at the Cost of Rs 498.96. If the Cost of White-washing is Rs 2.00 per Square Meter, Find the Concept: Volume of a Sphere.
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