9 votes 9 votes From a circular sheet of paper of radius $30$ cm, a sector of $10\%$ area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is _____ Quantitative Aptitude gate2015-ec-3 geometry quantitative-aptitude normal + – Akash Kanase asked Feb 12, 2016 edited Jun 1, 2019 by Lakshman Bhaiya Akash Kanase 5.8k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 10 votes 10 votes Let radius of circular sheet of paper $= R$ radius of the cone $=r$ height of cone $= H$ Perimeter of base of cone $= 0.9\times 2\pi R$ $\implies 2\pi r = 0.9*2\pi R$ $\implies r = 0.9R$ Now, height of cone $H = \sqrt{R^{2}-r^{2}}$ $\implies H = r.\sqrt{(R/r)^{2}-1}$ $\implies r/H= \frac{1}{\sqrt{(1/0.9)^{2}-1}}$ $= 2.06$ vijaycs answered May 12, 2016 edited Jun 18, 2019 by Arjun vijaycs comment Share Follow See all 4 Comments See all 4 4 Comments reply hileshkalal commented Jan 26, 2017 reply Follow Share Just one more thing, Question is asking about r/H = 1/0.48 = 2.08 3 votes 3 votes Ramij commented Aug 16, 2018 reply Follow Share but here it makes a conical surface ,,, how we use it as perimeter of base of the cone is equal to the 90% of the circular sheet.. it may be perimeter of the cone will be equal to the 90% area of the circle ,, isnt it?? correct me if i am wrong 0 votes 0 votes ankitgupta.1729 commented Dec 28, 2018 reply Follow Share how perimeter of the cone will be equal to the 90% area of the circle ? perimeter has some unit say meter whereas area has unit meter$^2$ then how both can be equal. If you are not getting it then solve it by taking area instead of perimeter. Since, $90\%$ area of the circular sheet is used to make canonical surface. So, $90\%$ area of the circular sheet = curved surface area of cone. $0.90 \times \pi R^{2} = \pi r l$ Now, here slant height $l$ will be same as radius of the circular sheet i.e. $R=30 \;cm$ So, $0.90 \times \pi R^{2} = \pi r R$ So, $r = 27$ Now, $h= \sqrt{l^{2}-r^{2}} = \sqrt{30^{2}-27^{2}} = 13.08$ So, $\frac{r}{h} = \frac{27}{13.08}$ = $2.06$ 21 votes 21 votes rohith1001 commented Apr 18, 2020 reply Follow Share Derivation of Surface Area of a cone(YouTube video) 3 votes 3 votes Please log in or register to add a comment.