Question : The ratio of the curved surface area of two cones is 1 : 4 and the ratio of slant height of the two cones is 2 : 1. What is the ratio of the radius of the two cones?
Option 1: 1 : 2
Option 2: 1 : 4
Option 3: 1 : 8
Option 4: 1 : 1
Correct Answer: 1 : 8
Solution : The curved surface area of a cone $ = \pi rl$ where \(r\) is the radius and \(l\) is the slant height of the cone. Given that the ratio of the curved surface areas of two cones = 1 : 4 $⇒\frac{\pi r_1 l_1}{\pi r_2 l_2} = \frac{1}{4}$ Also, given that the ratio of the slant heights of the two cones = 2 : 1 $⇒\frac{l_1}{l_2} = \frac{2}{1}$ $⇒\frac{r_1}{r_2} = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$ Hence, the correct answer is 1 : 8.
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Question : The ratio of curved surface areas of two cones is 1 : 8 and the ratio of their slant heights is 1 : 4. What is the ratio of radii of the two cones?
Option 1: 1 : 1
Option 2: 1 : 2
Option 3: 1 : 4
Option 4: 1 : 8
Question : A cylinder of height 8 cm and radius 6 cm is melted and converted into three cones of the same radius and height of the cylinder. Determine the total curved surface area of cones.
Option 1: $180 \pi\operatorname{cm^2}$
Option 2: $60 \pi\operatorname{cm^2}$
Option 3: $144 \pi\operatorname{cm^2}$
Option 4: $120 \pi\operatorname{cm^2}$
Question : The curved surface area of a cone whose base radius is 7 cm and slant height is 10 cm is:
Option 1: 280 cm2
Option 2: 250 cm2
Option 3: 300 cm2
Option 4: 220 cm2
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 : What is the curved surface area (in cm2) of a cylinder having a radius of base as 14 cm and height as 10 cm?
Option 1: 440
Option 2: 880
Option 3: 220
Option 4: 1320
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