Question : The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area (take $\pi$ = 3.14).
Option 1: 3391.2 cm2
Option 2: 5391.2 cm2
Option 3: 4391.2 cm2
Option 4: 5591.2 cm2
Correct Answer: 3391.2 cm2
Solution : Given, The ratio between the height and radius of the base of a cylinder is 7 : 5. Volume is 14836.5 cm3 Let the height be $7x$ and the radius be $5x$. According to the question, Volume of cylinder = $\pi r^2h$ ⇒ $14836.5 = \pi (5x)^2 × 7x$ ⇒ $14836.5 = (3.14)(25x^2) × 7x$ ⇒ $175x^3= \frac{14836.5}{3.14}$ ⇒ $x^3 = \frac{4725}{175}$ ⇒ $x^3 = 27$ $\therefore x = 3$ So, the radius $= 5x = 5 × 3 = 15$ cm and the height $= 7x = 7 × 3 = 21$ cm Now, the total surface area of the cylinder = $2\pi r(r + h)$ = 2 × (3.14) × 15 × (15 + 21) = 3391.2 cm2 Hence, the correct answer is 3391.2 cm2.
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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 height of a cylinder is $\frac{2}{3}$rd of its diameter. Its volume is equal to the volume of a sphere whose radius is 4 cm. What is the curved surface area (in cm2) of the cylinder?
Option 1: $\frac{112}{3} \pi$
Option 2: $32 \pi$
Option 3: $\frac{128}{3} \pi$
Option 4: $40 \pi$
Question : The radius of the base of a cylinder is 14 cm and its curved surface area is 880 cm2. Its volume (in cm3) is: (Take $\pi=\frac{22}{7}$)
Option 1: 3080
Option 2: 1078
Option 3: 6160
Option 4: 9240
Question : The radius of the base of a cylinder is 14 cm and its volume is 6160 cm3. The curved surface area (in cm2) is: (Take $\pi=\frac{22}{7}$)
Option 1: 778
Option 2: 880
Option 3: 660
Option 4: 940
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