Identify the given dimensions and calculate the outer radius.

Here are the solutions to the questions: Question 13: The length of a hollow cylinder Calvert is 5 m, its inner radius is 0.4 m and its outer diameter is 1.2 m. Take = 3.14. The volume of the material used to make it is: Step 1: Identify the given dimensions and calculate the outer radius. Length (height), h = 5 m Inner radius, r_i = 0.4 m Outer diameter, D_o = 1.2 m Outer radius, r_o = (D_o)/(2) = 1.2 m2 = 0.6 m Value of = 3.14 Step 2: Calculate the volume of the material. The volume of the material in a hollow cylinder is the difference between the outer cylinder's volume and the inner cylinder's volume. The formula for the volume of a cylinder is V = r^2 h. Volume of material, V_material = V_o - V_i = r_o^2 h - r_i^2 h = h (r_o^2 - r_i^2). Substitute the values: V_material = 3.14 × 5 m × ((0.6 m)^2 - (0.4 m)^2) V_material = 3.14 × 5 m × (0.36 m^2 - 0.16 m^2) V_material = 3.14 × 5 m × 0.20 m^2 V_material = 3.14 × 1 m^3 V_material = 3.14 m^3 Step 3: Convert the volume from cubic meters (m^3) to cubic decimeters (dm^3). We know that 1 m = 10 dm. Therefore, 1 m^3 = (10 dm)^3 = 1000 dm^3. V_material = 3.14 m^3 × 1000 dm^31 m^3 V_material = 3140 dm^3 The correct option is d) 3,140 dm^3. Question 14: A shopkeeper has a mixture of red sorghum flour and white sorghum flour weighing 40 kg. One type costs 1,900 FRW per kg and another cost 2,100 FRW per kg. If the mixture is sold at 2,000 FRW per kg, find the number of kg of each type. Step 1: Define variables and set up equations. Let x be the mass (in kg) of the red sorghum flour (costing 1,900 FRW/kg). Let y be the mass (in kg) of the white sorghum flour (costing 2,100 FRW/kg). The total mass of the mixture is 40 kg: x + y = 40 (1) The total cost of the mixture, if sold at 2,000 FRW/kg, is 40 kg × 2,000 FRW/kg = 80,000 FRW. The total cost of the ingredients must equal this total cost: 1900x + 2100y = 80,000 (2) Step 2: Solve the system of equations. From equation (1), express y in terms of x: y = 40 - x Substitute this expression for y into equation (2): 1900x + 2100(40 - x) = 80,000 1900x + 84000 - 2100x = 80,000 Combine like terms: -200x = 80,000 - 84000 -200x = -4000 Divide by -200: x = (-4000)/(-200) x = 20 kg Step 3: Find the value of y. Substitute x = 20 into y = 40 - x: y = 40 - 20 y = 20 kg So, there are 20 kg of red sorghum flour and 20 kg of white sorghum flour. The correct option is a) 20 kg and 20 kg. Question 15: The sum of interior angles of a regular polygon is 1440^. a) Find the number of sides of this polygon. b) Name the polygon. a) Find the number of sides of this polygon. Step 1: Use the formula for the sum of interior angles of a polygon. The sum of the interior angles (S) of a polygon with n sides is given by the formula: S = (n-2) × 180^ Given S = 1440^. Step 2: Substitute the given sum into the formula and solve for n. (n-2) × 180^ = 1440^ Divide both sides by 180^: n-2 = (1440)/(180) n-2 = 8 Add 2 to both sides: n = 8 + 2 n = 10 The number of sides of the polygon is 10. b) Name the polygon. A polygon with 10 sides is called a decagon. 3 done, 2 left today. You're making progress.