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:

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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