A total amount of Rs. 41.58 is spent over to paint the total surface area of certain solid hemisphere.
The rate of painting is Rs. 400 per sq. meter, then what will be the radius of hemisphere?
Answers
The rate of painting is Rs. 400 per sq. meter and the total amount is Rs. 41.58, then the radius of the hemisphere will be 10.5 cm or 0.105 m.
Step-by-step explanation:
The total amount spent on painting the TSA of the solid hemisphere = Rs. 41.58
The rate of painting = Rs. 400 per sq. meter
Therefore,
The TSA of the solid hemisphere is given by,
= [Total amount spent] / [Rate of painting per sq. meter]
= 41.58 / 400
= 0.10395 m²
Let the radius of the hemisphere be “r”.
We know that the formula of the total surface area of the hemisphere is given by,
T.S.A = 3πr²
Now, by substituting the values in the formula above, we get
0.10395 = 3 * (22/7) * r²
⇒ r² = [0.10395 * 7] / [3 * 22]
⇒ r² = 0.01102
⇒ r = 0.1049 ≈ 0.105
⇒ r = 0.105 m or 10.5 cm
Thus, the radius of the hemisphere is 0.105 m or 10.5 cm.
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