Quantitative Aptitude Ques 630
Question: A right angled sector of radius $ rcm $ is rolled up into a cone in such a way that two binding radii are joined together. Then, the curved surface area of the cone is
Options:
A) $ \pi r^{2}cm^{2} $
B) $ 4\pi r^{2}cm^{2} $
C) $ \frac{\pi r^{2}}{4}cm^{2} $
D) $ 2\pi r^{2}cm^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Length of arc, $ x=\frac{\theta }{360{}^\circ }\times 2\pi r $ $ x=\frac{\theta }{360{}^\circ }\times 2\pi r $
$ \Rightarrow $ $ x=\frac{90{}^\circ }{360{}^\circ }\times 2\pi r=\frac{\pi r}{2} $ Now, length of arc will be circumference of base and let radius of base be $ r _1. $
$ \therefore $ $ 2\pi r _1=x, $ $ 2\pi r _1=\frac{\pi r}{2} $ $ r _1=\frac{r}{4} $ and slant height $ =r $
$ \therefore $ Curved surface area $ =\pi r _1l=\pi \times \frac{r}{4}\times r=\frac{\pi r^{2}}{4}cm^{2} $
BETA
