IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 808 - 809 of 968

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Question number: 808

» Area, Surface Area & Volume

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Question

A sphere is placed in a cone of height 9 cm as shown in figure. The volume of sphere if it touches lateral surface and base of cone is________.

Ellipse c Ellipse c: Ellipse with foci A, B passing through C Ellipse c Ellipse c: Ellipse with foci A, B passing through C Circle d Circle d: Circle through H with center G Angle? Angle? : Angle between D, E, F Angle? Angle? : Angle between D, E, F Angle? Angle? : Angle between D, E, F Segment f Segment f: Segment [D, E] Segment g Segment g: Segment [E, F] Vector u Vector u: Vector [I, J] Vector u Vector u: Vector [I, J] Vector v Vector v: Vector [I, K] Vector v Vector v: Vector [I, K] Point D Point D: Point on c Point D Point D: Point on c Point E E = (7.42,2.4) Point E E = (7.42,2.4) Point F Point F: Point on c Point F Point F: Point on c Point G G = (7.46, -0.6) Point G G = (7.46, -0.6) 9 cm text1 = “9 cm”

Circle Inside a Triangle

A sphere is placed in a cone of height18cm. At angle 60 degree

Choices

Choice (4) Response

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b.

c.

d.

Question number: 809

» Triangle, Circle & Constructions

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In the given figure, FEBD is cyclic quadrilateral and AC is tangent to the circle with center ‘O’. ED is diameter, the ________.

Quadrilateral poly1 Quadrilateral poly1: Polygon D, B, E, F Circle c Circle c: Circle through B_1 with center O Angle? Angle? : Angle between A, B, D Angle? Angle? : Angle between A, B, D Angle? Angle? : Angle between A, B, D Angle? Angle? : Angle between D, E, F Angle? Angle? : Angle between D, E, F Angle? Angle? : Angle between D, E, F Segment c_1 Segment c_1: Segment [D, B] of Quadrilateral poly1 Segment d Segment d: Segment [B, E] of Quadrilateral poly1 Segment e Segment e: Segment [E, F] of Quadrilateral poly1 Segment f Segment f: Segment [F, D] of Quadrilateral poly1 Segment g Segment g: Segment [D, E] Vector u Vector u: Vector [B, C] Vector u Vector u: Vector [B, C] Vector v Vector v: Vector [B, A] Vector v Vector v: Vector [B, A] Point O O = (7.76, -0.34) Point O O = (7.76, -0.34) Point O O = (7.76, -0.34) Point D Point D: Point on c Point D Point D: Point on c Point D Point D: Point on c Point B Point B: Point on c Point B Point B: Point on c Point B Point B: Point on c Point E Point E: Point on c Point E Point E: Point on c Point E Point E: Point on c Point F Point F: Point on c Point F Point F: Point on c Point F Point F: Point on c Point C C = (10.78, -1.08) Point C C = (10.78, -1.08) Point C C = (10.78, -1.08) Point A A = (7.14,2.7) Point A A = (7.14,2.7) Point A A = (7.14,2.7)

FEBD is Cyclic Quadrilateral

FEBD is cyclic quadrilateral and AC is tangent to the circle with center ‘O’. ED is diameter, ∠DBA = 40°, ∠FED = 60°

Choices

Choice (4) Response

a.

b.

c.

d.