IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 723 - 724 of 968

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Question number: 723

» Area, Surface Area & Volume

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Question

is a line segment of length M is the mid-point of Circle are drawn with A, O and N as centers and radii (see figure). The area of the colored portion (in ) is________.

Image showing the Trapezoid and semi-circle

Image Showing the Trapezoid and Semi-Circle

AN is a line segment of length 2 cm. M is the mid-point of AN. Circle are drawn with A, O and N as centers and radii AM = MN

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 724

» Area, Surface Area & Volume

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The decorative block shown in figure is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge and the hemisphere fixed on the top has a diameter of . The total surface area of the block is________.

Quadrilateral poly1 Quadrilateral poly1: Polygon A, B, C, D Quadrilateral poly2 Quadrilateral poly2: Polygon A, E, F, B Quadrilateral poly3 Quadrilateral poly3: Polygon F, G, C, B Ellipse h Ellipse h: Ellipse with foci H, I passing through J Arc k Arc k: CircumcircularArc [H, K, I] Segment a Segment a: Segment [A, B] of Quadrilateral poly1 Segment b Segment b: Segment [B, C] of Quadrilateral poly1 Segment c Segment c: Segment [C, D] of Quadrilateral poly1 Segment d Segment d: Segment [D, A] of Quadrilateral poly1 Segment a_1 Segment a_1: Segment [A, E] of Quadrilateral poly2 Segment e Segment e: Segment [E, F] of Quadrilateral poly2 Segment f Segment f: Segment [F, B] of Quadrilateral poly2 Segment b_1 Segment b_1: Segment [B, A] of Quadrilateral poly2 Segment f_1 Segment f_1: Segment [F, G] of Quadrilateral poly3 Segment g Segment g: Segment [G, C] of Quadrilateral poly3 Segment c_1 Segment c_1: Segment [C, B] of Quadrilateral poly3 Segment b_2 Segment b_2: Segment [B, F] of Quadrilateral poly3 Vector u Vector u: Vector [L, M] Vector u Vector u: Vector [L, M] Vector v Vector v: Vector [N, O] Vector v Vector v: Vector [N, O] Vector w Vector w: Vector [S, T] Vector w Vector w: Vector [S, T] Vector i Vector i: Vector [S, U] Vector i Vector i: Vector [S, U] 6 cm text1 = “6 cm” 3.2 cm text2 = “3.2 cm”

The Decorative Block

The decorative block is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge 6 cm, and the hemisphere fixed on the top has a diameter of 3.2 cm

Choices

Choice (4) Response

a.

b.

c.

d.