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: $120 \pi\operatorname{cm^2}$
Correct Answer: $180 \pi\operatorname{cm^2}$
Solution :
The radius ($r$) of each cone = radius of the cylinder = 6 cm
The height ($h$) of each cone = height of the cylinder = 8 cm
The curved surface area of a cone, where $l$ is the slant height of the cone $= \pi r l$
Now, $l = \sqrt{r^2 + h^2}= \sqrt{(6)^2 + (8)^2} = 10 \text{ cm}$
The curved surface area of a cone, where $l$ is the slant height of the cone $= \pi r l$
So, the curved surface area of each cone,
$= \pi (6) (10) = 60\pi \text{ cm}^2$
Since there are 3 cones, the total curved surface area,
$= 3 \times 60\pi = 180\pi \text{ cm}^2$
Hence, the correct answer is $180\pi \text{ cm}^2$.
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