Question : The cost of painting the total surface area of a 30 m high solid right circular cylinder at the rate of Rs. 25 per m2 is Rs. 18,425. What is the volume (in m3) of this cylinder [use $\pi=\frac{22}{7}$ ]?
Option 1: 1145
Option 2: 1210
Option 3: 1155
Option 4: 1122
Correct Answer: 1155
Solution :
The total surface area of a right circular cylinder is given by the formula:
$⇒\text{Area} = 2\pi r(r + h)$
Where \(r\) is the radius of the base of the cylinder and \(h\) is the height of the cylinder.
Given that the cost of painting the total surface area of the cylinder is Rs. 18,425 at the rate of Rs. 25 per m², we can find the total surface area:
$⇒\text{Area} = \frac{\text{Cost}}{\text{Rate}} = \frac{{18425}}{{25}} = 737 \text{ m}^2$
Substituting the given height \(h = 30\) m and \(\pi = \frac{{22}}{{7}}\) into the formula, we can solve for the radius \(r\):
$⇒737 = 2 \times \frac{{22}}{{7}} \times r \times (r + 30)$
$⇒4r^2+120r-469=0$
$⇒(2r+67)(2r-7)=0$
$⇒r=3.5$ m
The volume of a right circular cylinder is,
$⇒\text{Volume} = \pi r^2 h$
$⇒\text{Volume} = \frac{{22}}{{7}} \times 3.5^2 \times 30 = 1155 \text{ m}^2$
Hence, the correct answer is 1155.
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