This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Step 1: Address Question 28 (Part 1). The question "a circle of radius 17 cm. Find the distance between the chords." is incomplete. To find the distance between chords, their lengths or other properties must be provided. Step 2: Address Question 28 (Part 2). Find the square metres of canvas required for a conical tent with height h = 3.5 m and base radius r = 12 m. The canvas required is the lateral surface area of the cone, given by A = r l, where l is the slant height. First, calculate the slant height l: l = sqrt(r^2 + h^2) l = sqrt((12)^2 + (3.5)^2) l = sqrt(144 + 12.25) l = sqrt(156.25) l = 12.5 m Now, calculate the lateral surface area: A = × 12 m × 12.5 m A = 150 m^2 Using ≈ 3.14159: A ≈ 150 × 3.14159 m^2 A ≈ 471.2385 m^2 The canvas required is 150 m^2 or approximately 471.24 m^2. Step 3: Address Question 29 (Part 1). The surface areas of two spheres are in the ratio 1:4. Find the ratio of their volumes. Let the radii of the two spheres be r_1 and r_2. The surface area of a sphere is A = 4 r^2. Given (A_1)/(A_2) = (4 r_1^2)/(4 r_2^2) = (1)/(4). (r_1^2)/(r_2^2) = (1)/(4) ((r_1)/(r_2))^2 = (1)/(4) Taking the square root of both sides: (r_1)/(r_2) = sqrt((1)/(4)) = (1)/(2) The volume of a sphere is V = (4)/(3) r^3. The ratio of their volumes is: (V_1)/(V_2) = (4)/(3) r_1^3(4)/(3) r_2^3 = (r_1^3)/(r_2^3) = ((r_1)/(r_2))^3 Substitute the ratio of radii: (V_1)/(V_2) = ((1)/(2))^3 = (1)/(8) The ratio of their volumes is 1:8. Step 4: Address Question 29 (Part 2). In the given figure, AB CD. Find the value of x, y and z. Given: • Line AB is parallel to line CD. • AEF = 75^. • EGD = 125^. • x = EFG, y = FGE, z = FEG. 1. Find x: Since AB CD, and EF is a transversal, AEF and EFG are alternate interior angles. Therefore, EFG = AEF. x = 75^ 2. Find y: Since AB CD, and EG is a transversal, EGD and FGE are angles on a straight line with the angle adjacent to EGD on line CD. The angle FGE and EGD are not directly related as alternate interior or corresponding. However, FGE and EGC are supplementary if G is on CD. The angle FGE is part of the triangle. The angle EGC is 180^ - EGD (angles on a straight line). EGC = 180^ - 125^ = 55^. So, y = FGE = 55^. 3. Find z: The sum of angles in a triangle is 180^. In EFG: FEG + EFG + FGE = 180^ z + x + y = 180^ z + 75^ + 55^ = 180^ z + 130^ = 180^ z = 180^ - 130^ z = 50^ The values are x = 75^, y = 55^, z = 50^. Step 5: Address Question 30.