a quadrant of a circle of radius 7cm is rolled into a cone find the slant height and the - Maths - Surface Areas and Volumes

Question

a quadrant of a circle of radius 7cm is rolled into a cone find
the slant height and the height of the cone

Ankush Jain · Accepted Answer

Let the quadrant OAB of a circle be rolled to form a cone

Given radius of circle, r = 7 cm When quadrant of a circle is rolled to form a cone, than slant height of the cone must be equal to radius of the circle

â‡’ l = r = 7 cm According to given question, Area of quadrant of circle = Curved surface area of cone $\Rightarrow \frac{1}{4} \times (Area of circle) = π R l \Rightarrow \frac{1}{4} \times (π r^{2}) = π R l \Rightarrow \frac{(7)^{2}}{4} = R (7) \Rightarrow R= \frac{7}{4} cm= 1 75 cm$ We know that, $Slant height = \sqrt{(height)^{2} + (Radius)^{2}} \Rightarrow l = \sqrt{h^{2} + R^{2}} 7 = \sqrt{h^{2} + (1 75)^{2}}$ Squaring both sides, we get 49 = h2 + (1 75)2 â‡’ h2 = 49 â€“ 3 0625 h2 =45 9375 â‡’ h = 6 77 cm

a quadrant of a circle of radius 7cm is rolled into a cone. find the slant height and the height of the cone.