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Maths-

General

Easy

Question

A dome of a building is in the form of a hemisphere. From inside it was white washed at the cost of RS 4989.60. If the cost of white washing is Rs 20 per square metre , find the i) inside surface area of the dome ii) Volume of the air inside the dome

hint Hint:

Volume of hemisphere is $equals 2 over 3 pi r cubed$

The correct answer is: 179.67cm3

Explanation:

We have given a dome of a building is in the form of a hemisphere. From inside it was white washed at the cost of . If the cost of white washing is per square metre.

We have to find the (i) Inside surface area of dome. (ii) Volume of the air inside the dome

Step 1 of 1:
It is given that the total cost of white washing is Rs 4989.60.
The cost of white washing per unit square meter is Rs 20.
So,
Total inside surface area will be
= $fraction numerator T o t a l space cos t over denominator C o s t space p e r space u n i t space a r e a end fraction$
= $fraction numerator 4929.60 over denominator 20 end fraction$
= 246.48m²
Step 2 of 2:
Now inside surface area is 246.48m²
$2 pi r squared equals 246.48 m squared$
r² = 39.22
r = 6.26
So, The volume will be
$V equals 2 over 3 pi r cubed$
$equals 2 over 3 pi left parenthesis 6.26 right parenthesis cubed$
= 82.07
Hence, The inside surface area is 246.48m² and the inside volume is 82.07m³

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