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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Question : The total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm3
Option 2: 3696 cm3
Option 3: 4002 cm3
Option 4: 4851 cm3
Question : The ratio of the radius of the base and the height of a solid right circular cylinder is 2 : 3. If its volume is 202.125 cm3, then its total surface area is: (Take $\pi=\frac{22}{7}$)
Option 1: 192.5 cm2
Option 2: 154 cm2
Option 3: 168 cm2
Option 4: 115.5 cm2
Question : The curved surface area of a solid cylinder of height 15 cm is 660 cm2. What is the volume (in cm3) of the cylinder? $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
Option 1: 2060
Option 2: 2540
Option 3: 2310
Option 4: 3210
Question : What is the total surface area of a solid right circular cylinder of radius 7 cm and height 8 cm?$(\pi=\frac{22}{7})$
Option 1: 560 cm2
Option 2: 660 cm2
Option 3: 850 cm2
Option 4: 760 cm2
Question : The volume of a solid right circular cone is $600 \pi \;\text{cm}^3$ and the diameter of its base is 30 cm. The total surface area (in cm2) of the cone is:
Option 1: $480 \pi$
Option 2: $255 \pi$
Option 3: $472 \pi$
Option 4: $496 \pi$
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